Characterizations of Hardy-type, Bergman-type and Dirichlet-type spaces on certain classes of complex-valued functions (original) (raw)

On characterizations of Bloch-type, Hardy-type and Lipschitz-type spaces

Mathematische Zeitschrift, 2014

In this paper, we establish a Bloch-type growth theorem for generalized Bloch-type spaces and discuss relationships between Dirichlet-type spaces and Hardy-type spaces on certain classes of complex-valued functions. Then we present some applications to non-homogeneous Yukawa PDEs. We also consider some properties of the Lipschitz-type spaces on certain classes of complex-valued functions. Finally, we will study a class of composition operators on these spaces.

Estimates on Some General Classes of Holomorphic Function Spaces

Symmetry

In this current manuscript, some general classes of weighted analytic function spaces in a unit disc are defined and studied. Special functions significant in both analytic T(p,q,m,s;Ψ) norms and analytic Ψ-Bloch norms serve as a framework for introducing new families of analytic classes. An application in operator theory is provided by establishing important properties of the composition-type operator Cϕ such as the boundedness and compactness with the help of the defined new classes.

Two Elementary Analytic Functions and Their Relationship with Hardy and Bergman Spaces

2018

In this paper, we start by proving that the function which is holomorphic in the open unit disc centred at the origin, is an element of a Hardy space if and only if Here we give a new proof for a known result. Moreover, the present work provides two different new proofs for one of the implications mentioned above. One proves that the same function is an element of a Bergman space if and only if This is the first completely new result of this work. From these theorems we deduce the behavior of the function in the half – open disc Although the assertions claimed above refer to complex analytic functions, and the involved spaces are function spaces of analytic complex functions, the proofs from below are based on results and methods of real analysis.

Some Analytic Classes of Banach Function Spaces

We introduce a new class of functions, called the SK(p, q)−type spaces of analytic functions in the unit disk, then we give some characterizations of Bergman spaces by our SK(p, q) spaces.

Holomorphic N K and Bergman-type spaces

Birkh¨auser Verlarg Publisher Basel/Switzerland, 2008

In this paper we introduce a new class of functions, called NK-type space of analytic functions by the help of a nondecreasing function K : [0, ∞) → [0, ∞). Further, under mild conditions on the weight function K we characterize lacunary series in NK space. Finally, we study the boundedness and compactness of composition operators between NK and Bergman spaces. Mathematics Subject Classification (2000). Primary 47B33; 47B38 Secondary 30H05.

Spaces of analytic functions of Hardy-Bloch type

Journal D Analyse Mathematique, 2006

For 0 < p ≤ ∞ and 0 < q ≤ ∞, the space of Hardy-Bloch type B(p, q) consists of those functions f which are analytic in the unit disk D such that (1 − r)Mp(r, f ) ∈ L q (dr/(1 − r)). We note that B(∞, ∞) coincides with the Bloch space B and that B ⊂ B(p, ∞), for all p. Also, the space B(p, p) is the Dirichlet space D p p−1 . We prove a number of results on decomposition of spaces with logarithmic weights which allow us to obtain sharp results about the mean growth of the B(p, q)-functions. In particular, we prove that if f is an analytic function in D and 2 ≤ p < ∞, then the condition Mp(r, f ) = O (1 − r) −1 ¡ , as r → 1, implies that Mp(r, f ) = O log 1 1−r 1/2 , as r → 1. This result is an improvement of the well known estimate of Clunie and MacGregor and Makarov about the integral means of Bloch functions, and it also improves the main result in a recent paper by Girela and Peláez. We also consider the question of characterizing the univalent functions in the spaces B(p, 2), 0 < p < ∞, and in some other related spaces and give some applications of our estimates to study the Carleson measures for the spaces B(p, 2) and D p p−1 . D |f (z)| p dA(z) < ∞ 2000 Mathematics Subject Classification. 30D45, 30D55.

New Characterizations of Bergman Spaces

Ann. Acad. Sci. Fenn. Math, 2008

We obtain several new characterizations for the standard weighted Bergman spaces A p α on the unit ball of C n in terms of the radial derivative, the holomorphic gradient, and the invariant gradient.

On the Boundary Behavior of Functions in Spaces of Hardy Type

Mathematics of the USSR-Izvestiya, 1991

The spaces ^p(3f, Γ, μ) consisting of functions u continuous on Sf with / r a£ L p are introduced, along with the subspaces of them consisting of the functions having a Γ-limit a.e. The properties of the spaces βί" ρ and the action in them of operators of smoothing type are studied. The results are applied to Hardy spaces of harmonic or holomorphic functions.