Houyu JIA - Academia.edu (original) (raw)

Papers by Houyu JIA

Research paper thumbnail of Boundedness of admissible area function on nonisotropic Lipschitz space

Proceedings of the American Mathematical Society, 2004

Let B be the unit ball in C n , let S be the unit sphere, and let S β (f) be the admissible area ... more Let B be the unit ball in C n , let S be the unit sphere, and let S β (f) be the admissible area function. In this paper, we show that if f ∈ Lipα(S), then S β (f) ∈ Lipα(S) and there exists a constant C such that S β (f) Lipα ≤ C f Lipα .

Research paper thumbnail of Long time existence of classical solutions for the rotating Euler equations and related models in the optimal Sobolev space

Research paper thumbnail of Global well-posedness for the 3D Navier–Sokes equations with a large component of vorticity

Journal of Mathematical Analysis and Applications, 2019

In this paper, we give a new approach to improve the Leray's result concerning the cauchy problem... more In this paper, we give a new approach to improve the Leray's result concerning the cauchy problem to the 3D Navier-Stokes equations. In particular, global wellposedness with a large component of the initial vorticity is obtained. Our idea is considering the vorticity equations and using some suitable function spaces.

Research paper thumbnail of Local well-posedness for the generalized surface quasi-geostrophic equation with singular velocity in optimal space

Journal of Mathematical Analysis and Applications, 2016

For standard inviscid surface quasi-geostrophic (SQG) equation, it is well-known that H 2 (R 2) i... more For standard inviscid surface quasi-geostrophic (SQG) equation, it is well-known that H 2 (R 2) is the borderline space when we consider the corresponding local wellposedness. In this paper, we study a new generalized SQG equation with the singular velocity u = ∇ ⊥ Λ −2+α (log(I − Δ)) μ θ, 1 < α < 2, μ > 0. We find the borderline space is H 1+α (R 2), which is consistent with the standard SQG equation when α = 1, μ = 0. This result can be seen as an extensive work of [3], which depends on a new observation.

Research paper thumbnail of Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels

Frontiers of Mathematics in China, 2015

Research paper thumbnail of Compact characterizations of composition operators on Bergman space

Let Ω be a bounded strongly pseudoconvex domain in C\+ n,A\+p(Ω) be the Bergman space, Cφ:A p(Ω)... more Let Ω be a bounded strongly pseudoconvex domain in C\+ n,A\+p(Ω) be the Bergman space, Cφ:A p(Ω)→A p(Ω) be a compsition operator.In this paper,some characterizations of the compactness of Cφ are given.

Research paper thumbnail of The characterizations of the Carleson measure and the Bloch space

Research paper thumbnail of Unique continuation and Schrödinger equation

In this paper, the authors study the solution of a certain Schrodinger equation:Lu = -div(A(x)u) ... more In this paper, the authors study the solution of a certain Schrodinger equation:Lu = -div(A(x)u) + V(x)u(x) = 0with Lipschitz continuous A(x) and singular potential V(x). and prove the unique continu-ation properties (ucp.) for solution and the absolute value of solution belongs to some Ap weight.

Research paper thumbnail of Local Hardy spaces and inhomogeneous Dirichlet problems in exterior regular domains

At first we give an atomic decomposition of the local Hardy spaces h r p (Ω) (0<p≤1) and their... more At first we give an atomic decomposition of the local Hardy spaces h r p (Ω) (0<p≤1) and their dual spaces, where the domain Ω is exterior regular in ℝ n (n≥3). Then for given data f∈h r p (Ω), we discuss the inhomogeneous Dirichlet problems Lu=finΩu=0on∂Ω(1) where the operator L is uniformly elliptic. Also we obtain estimates for the Green potential in local Hardy spaces h r p (Ω).

Research paper thumbnail of Boundedness of commutators of maximal function on Morrey spaces

Research paper thumbnail of Boundedness on general Morrey spaces of the commutators generated by maximal function

Research paper thumbnail of Weighted Triebel-Lizorkin boundedness for rough singular integral

This paper studies the weighted boundedness on Triebel - Lizorkin spaces for the rough singular i... more This paper studies the weighted boundedness on Triebel - Lizorkin spaces for the rough singular integral. When kernel Ω(x') ∈ L log+ L(Sn-1), for certain radial weight function w(x), the weighted boundedness of the operator is established. Meanwhile, the authors obtain the Fp α,q(w) weighted boundedness of the above operator with Muckenhopt weight function while Ω ∈ Lr(Sn-1), 1 r ≤ ∞.

Research paper thumbnail of Boundedness of CRW type commutators on Triebel-Lizorkin spaces

In this paper,the behavior of the commutator of singular integral operator on the Triebel-Lizorki... more In this paper,the behavior of the commutator of singular integral operator on the Triebel-Lizorkin spaces (?)(R~n)is considered.The authors obtain the equivalent conditions to (?)(R~n)(s＞0)boundedness of the commutator [b,T],where b∈BMO(R~n) and T is convolution operator with rough kernel Ω∈L log~+L(S~(n-1)).

Research paper thumbnail of Boundedness of Commutators of High-Dimensional Hausdorff Operators

Journal of Function Spaces and Applications, 2012

Research paper thumbnail of On non-linear elliptic equation with weight

Nonlinear Analysis: Theory, Methods & Applications, 2005

ABSTRACT In this paper, we prove the existence and uniqueness theorem of the Dirichlet problem fo... more ABSTRACT In this paper, we prove the existence and uniqueness theorem of the Dirichlet problem for certain non-linear elliptic operators with Muckenhoupt weight.

Research paper thumbnail of Local well-posedness for the 2D non-dissipative quasi-geostrophic equation in Besov spaces

Nonlinear Analysis: Theory, Methods & Applications, 2009

In this paper we prove the local-in-time well-posedness for the 2D non-dissipative quasi-geostrop... more In this paper we prove the local-in-time well-posedness for the 2D non-dissipative quasi-geostrophic equation, and study the blow-up criterion in the critical Besov spaces. These results improve the previous one by Constantin et al. [P. Constantin, A. Majda, E. Tabak, Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar, Nonlinearity 7 (1994) 1495–1533].

Research paper thumbnail of Singular integral operator, Hardy-Morrey space estimates for multilinear operators and Navier-Stokes equations

Mathematical Methods in the Applied Sciences, 2010

After establishing the molecule characterization of the Hardy-Morrey space, we prove the boundedn... more After establishing the molecule characterization of the Hardy-Morrey space, we prove the boundedness of the singular integral operator and the Riesz potential. We also obtain the Hardy-Morrey space estimates for multilinear operators satisfying certain vanishing moments. As an application, we study the existence and the uniqueness of the solutions to the Navier-Stokes equations for the initial data in the Hardy-Morrey space HM p q (p n) for q as small as possible. Here, the Hardy-Morrey space estimates for multilinear operators are important tools.

Research paper thumbnail of Existence of suitable weak solutions of complex Ginzburg–Landau equations and properties of the set of singular points

Journal of Mathematical Physics, 2003

In this paper, we consider the supercritical complex Ginzburg-Landau equation. We discuss the exi... more In this paper, we consider the supercritical complex Ginzburg-Landau equation. We discuss the existence of suitable weak solution in ⍀, where ⍀ is a bounded domain in R n or the whole space. We also discuss the properties of the set of the singular points of the suitable weak solution in R n , which means that the possible singular points are located in a bounded ball for any given time and there is no singular point on the whole space after limited time.

Research paper thumbnail of Boundedness of rough oscillatory singular integral on Triebel–Lizorkin spaces

Journal of Mathematical Analysis and Applications, 2005

We give the boundedness on Triebel-Lizorkin spaces for oscillatory singular integral operators wi... more We give the boundedness on Triebel-Lizorkin spaces for oscillatory singular integral operators with polynomial phases and rough kernels of the form e iP (x) Ω(x)|x| −n , where Ω ∈ L log + L(S n−1) is homogeneous of degree zero and satisfies certain cancellation condition.

Research paper thumbnail of Boundedness of certain commutators on Triebel–Lizorkin spaces

Journal of Mathematical Analysis and Applications, 2007

In this paper, two types of commutators are considered, and the boundedness of these operators on... more In this paper, two types of commutators are considered, and the boundedness of these operators on Triebel-Lizorkin spaces are discussed.

Research paper thumbnail of Boundedness of admissible area function on nonisotropic Lipschitz space

Proceedings of the American Mathematical Society, 2004

Let B be the unit ball in C n , let S be the unit sphere, and let S β (f) be the admissible area ... more Let B be the unit ball in C n , let S be the unit sphere, and let S β (f) be the admissible area function. In this paper, we show that if f ∈ Lipα(S), then S β (f) ∈ Lipα(S) and there exists a constant C such that S β (f) Lipα ≤ C f Lipα .

Research paper thumbnail of Long time existence of classical solutions for the rotating Euler equations and related models in the optimal Sobolev space

Research paper thumbnail of Global well-posedness for the 3D Navier–Sokes equations with a large component of vorticity

Journal of Mathematical Analysis and Applications, 2019

In this paper, we give a new approach to improve the Leray's result concerning the cauchy problem... more In this paper, we give a new approach to improve the Leray's result concerning the cauchy problem to the 3D Navier-Stokes equations. In particular, global wellposedness with a large component of the initial vorticity is obtained. Our idea is considering the vorticity equations and using some suitable function spaces.

Research paper thumbnail of Local well-posedness for the generalized surface quasi-geostrophic equation with singular velocity in optimal space

Journal of Mathematical Analysis and Applications, 2016

For standard inviscid surface quasi-geostrophic (SQG) equation, it is well-known that H 2 (R 2) i... more For standard inviscid surface quasi-geostrophic (SQG) equation, it is well-known that H 2 (R 2) is the borderline space when we consider the corresponding local wellposedness. In this paper, we study a new generalized SQG equation with the singular velocity u = ∇ ⊥ Λ −2+α (log(I − Δ)) μ θ, 1 < α < 2, μ > 0. We find the borderline space is H 1+α (R 2), which is consistent with the standard SQG equation when α = 1, μ = 0. This result can be seen as an extensive work of [3], which depends on a new observation.

Research paper thumbnail of Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels

Frontiers of Mathematics in China, 2015

Research paper thumbnail of Compact characterizations of composition operators on Bergman space

Let Ω be a bounded strongly pseudoconvex domain in C\+ n,A\+p(Ω) be the Bergman space, Cφ:A p(Ω)... more Let Ω be a bounded strongly pseudoconvex domain in C\+ n,A\+p(Ω) be the Bergman space, Cφ:A p(Ω)→A p(Ω) be a compsition operator.In this paper,some characterizations of the compactness of Cφ are given.

Research paper thumbnail of The characterizations of the Carleson measure and the Bloch space

Research paper thumbnail of Unique continuation and Schrödinger equation

In this paper, the authors study the solution of a certain Schrodinger equation:Lu = -div(A(x)u) ... more In this paper, the authors study the solution of a certain Schrodinger equation:Lu = -div(A(x)u) + V(x)u(x) = 0with Lipschitz continuous A(x) and singular potential V(x). and prove the unique continu-ation properties (ucp.) for solution and the absolute value of solution belongs to some Ap weight.

Research paper thumbnail of Local Hardy spaces and inhomogeneous Dirichlet problems in exterior regular domains

At first we give an atomic decomposition of the local Hardy spaces h r p (Ω) (0<p≤1) and their... more At first we give an atomic decomposition of the local Hardy spaces h r p (Ω) (0<p≤1) and their dual spaces, where the domain Ω is exterior regular in ℝ n (n≥3). Then for given data f∈h r p (Ω), we discuss the inhomogeneous Dirichlet problems Lu=finΩu=0on∂Ω(1) where the operator L is uniformly elliptic. Also we obtain estimates for the Green potential in local Hardy spaces h r p (Ω).

Research paper thumbnail of Boundedness of commutators of maximal function on Morrey spaces

Research paper thumbnail of Boundedness on general Morrey spaces of the commutators generated by maximal function

Research paper thumbnail of Weighted Triebel-Lizorkin boundedness for rough singular integral

This paper studies the weighted boundedness on Triebel - Lizorkin spaces for the rough singular i... more This paper studies the weighted boundedness on Triebel - Lizorkin spaces for the rough singular integral. When kernel Ω(x') ∈ L log+ L(Sn-1), for certain radial weight function w(x), the weighted boundedness of the operator is established. Meanwhile, the authors obtain the Fp α,q(w) weighted boundedness of the above operator with Muckenhopt weight function while Ω ∈ Lr(Sn-1), 1 r ≤ ∞.

Research paper thumbnail of Boundedness of CRW type commutators on Triebel-Lizorkin spaces

In this paper,the behavior of the commutator of singular integral operator on the Triebel-Lizorki... more In this paper,the behavior of the commutator of singular integral operator on the Triebel-Lizorkin spaces (?)(R~n)is considered.The authors obtain the equivalent conditions to (?)(R~n)(s＞0)boundedness of the commutator [b,T],where b∈BMO(R~n) and T is convolution operator with rough kernel Ω∈L log~+L(S~(n-1)).

Research paper thumbnail of Boundedness of Commutators of High-Dimensional Hausdorff Operators

Journal of Function Spaces and Applications, 2012

Research paper thumbnail of On non-linear elliptic equation with weight

Nonlinear Analysis: Theory, Methods & Applications, 2005

ABSTRACT In this paper, we prove the existence and uniqueness theorem of the Dirichlet problem fo... more ABSTRACT In this paper, we prove the existence and uniqueness theorem of the Dirichlet problem for certain non-linear elliptic operators with Muckenhoupt weight.

Research paper thumbnail of Local well-posedness for the 2D non-dissipative quasi-geostrophic equation in Besov spaces

Nonlinear Analysis: Theory, Methods & Applications, 2009

In this paper we prove the local-in-time well-posedness for the 2D non-dissipative quasi-geostrop... more In this paper we prove the local-in-time well-posedness for the 2D non-dissipative quasi-geostrophic equation, and study the blow-up criterion in the critical Besov spaces. These results improve the previous one by Constantin et al. [P. Constantin, A. Majda, E. Tabak, Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar, Nonlinearity 7 (1994) 1495–1533].

Research paper thumbnail of Singular integral operator, Hardy-Morrey space estimates for multilinear operators and Navier-Stokes equations

Mathematical Methods in the Applied Sciences, 2010

After establishing the molecule characterization of the Hardy-Morrey space, we prove the boundedn... more After establishing the molecule characterization of the Hardy-Morrey space, we prove the boundedness of the singular integral operator and the Riesz potential. We also obtain the Hardy-Morrey space estimates for multilinear operators satisfying certain vanishing moments. As an application, we study the existence and the uniqueness of the solutions to the Navier-Stokes equations for the initial data in the Hardy-Morrey space HM p q (p n) for q as small as possible. Here, the Hardy-Morrey space estimates for multilinear operators are important tools.

Research paper thumbnail of Existence of suitable weak solutions of complex Ginzburg–Landau equations and properties of the set of singular points

Journal of Mathematical Physics, 2003

In this paper, we consider the supercritical complex Ginzburg-Landau equation. We discuss the exi... more In this paper, we consider the supercritical complex Ginzburg-Landau equation. We discuss the existence of suitable weak solution in ⍀, where ⍀ is a bounded domain in R n or the whole space. We also discuss the properties of the set of the singular points of the suitable weak solution in R n , which means that the possible singular points are located in a bounded ball for any given time and there is no singular point on the whole space after limited time.

Research paper thumbnail of Boundedness of rough oscillatory singular integral on Triebel–Lizorkin spaces

Journal of Mathematical Analysis and Applications, 2005

We give the boundedness on Triebel-Lizorkin spaces for oscillatory singular integral operators wi... more We give the boundedness on Triebel-Lizorkin spaces for oscillatory singular integral operators with polynomial phases and rough kernels of the form e iP (x) Ω(x)|x| −n , where Ω ∈ L log + L(S n−1) is homogeneous of degree zero and satisfies certain cancellation condition.

Research paper thumbnail of Boundedness of certain commutators on Triebel–Lizorkin spaces

Journal of Mathematical Analysis and Applications, 2007

In this paper, two types of commutators are considered, and the boundedness of these operators on... more In this paper, two types of commutators are considered, and the boundedness of these operators on Triebel-Lizorkin spaces are discussed.