A characterization for BBB-singular integral operator and its commutators on generalized weighted BBB-Morrey spaces (original) (raw)
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Mathematical Inequalities & Applications
We consider the generalized weighted Morrey spaces M p(•),ϕ ω (Ω) with variable exponent p(x) and a general function ϕ(x,r) defining the Morrey-type norm. In case of unbounded sets Ω ⊂ R n we prove the boundedness of the Hardy-Littlewood maximal operator and Calderón-Zygmund singular operators with standard kernel, in such spaces. We also prove the boundedness of the commutators of maximal operator and Calderón-Zygmund singular operators in the generalized weighted Morrey spaces with variable exponent Mathematics subject classification (2010): 42B20, 42B25, 42B35.
Hacettepe journal of mathematics and statistics, 2023
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In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear operators including many interesting in harmonic analysis and its commutators on the weighted Morrey spaces. Finally, as an application, the boundedness of strongly singular integral operators and commutators with symbols in BMO space are also given.
Weighted Hardy and singular operators in Morrey spaces
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We study the weighted boundedness of the Cauchy singular integral operator S Γ in Morrey spaces L p,λ (Γ) on curves satisfying the arc-chord condition, for a class of "radial type" almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces L p,λ (0, ℓ), ℓ > 0. We find conditions for weighted Hardy operators to be bounded in Morrey spaces. To cover the case of curves we also extend the boundedness of the Hardy-Littlewood maximal operator in Morrey spaces, known in the Euclidean setting, to the case of Carleson curves.
Integral operators commuting with dilations and rotations in generalized Morrey‐type spaces
Mathematical Methods in the Applied Sciences, 2020
We find conditions for the boundedness of integral operators K commuting with dilations and rotations in a local generalized Morrey space. We also show that under the same conditions, these operators preserve the subspace of such Morrey space, known as vanishing Morrey space. We also give necessary conditions for the boundedness when the kernel is non-negative. In the case of classical Morrey spaces, the obtained sufficient and necessary conditions coincide with each other. In the one-dimensional case, we also obtain similar results for global Morrey spaces. In the case of radial kernels, we also obtain stronger estimates of K via spherical means of. We demonstrate the efficiency of the obtained conditions for a variety of examples such as weighted Hardy operators, weighted Hilbert operator, their multidimensional versions, and others. KEYWORDS dilation invariant operators, generalized Morrey spaces, Hardy operators, Hilbert operator, operators with homogeneous kernels, rotation invariant operators, Matuszewska-Orlicz indices, vanishing generalized Morrey spaces MSC CLASSIFICATION 46E30; 46E35 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Calderón–Zygmund Type Singular Operators in Weighted Generalized Morrey Spaces
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We find conditions for the weighted boundedness of a general class of multidimensional singular integral operators in generalized Morrey spaces L p,ϕ (R n , w), defined by a function ϕ(x, r) and radial type weight w(|x − x 0 |), x 0 ∈ R n. These conditions are given in terms of inclusion into L p,ϕ (R n , w), of a certain integral constructions defined by ϕ and w. In the case of ϕ = ϕ(r) we also provide easy to check sufficient conditions for that in terms of indices of ϕ and w.