Hausdorff and Quasi-Hausdorff Matrices on Spaces of Analytic Functions

2006 ◽  
Vol 58 (3) ◽  
pp. 548-579 ◽  
Author(s):  
P. Galanopoulos ◽  
M. Papadimitrakis
Keyword(s):  
Analytic Functions ◽  
Bergman Spaces ◽  
Dirichlet Space ◽  
Moment Sequence ◽  
Bloch Spaces ◽  
The Matrix ◽  
Generating Sequence ◽  
Hausdorff Matrices ◽  
The Moment ◽  
Spaces Of Analytic Functions

AbstractWe consider Hausdorff and quasi-Hausdorff matrices as operators on classical spaces of analytic functions such as the Hardy and the Bergman spaces, the Dirichlet space, the Bloch spaces and BMOA. When the generating sequence of the matrix is the moment sequence of a measure μ, we find the conditions on μ which are equivalent to the boundedness of the matrix on the various spaces.

scholarly journals Variable Exponent Spaces of Analytic Functions

2020 ◽  
Author(s):  
Gerardo A. Chacón ◽  
Gerardo R. Chacón
Keyword(s):  
Hardy Spaces ◽  
Measurable Function ◽  
Analytic Functions ◽  
Variable Exponent ◽  
Bergman Spaces ◽  
Lebesgue Spaces ◽  
Basic Properties ◽  
Variable Exponent Spaces ◽  
Real Functions ◽  
Spaces Of Analytic Functions

Variable exponent spaces are a generalization of Lebesgue spaces in which the exponent is a measurable function. Most of the research done in this topic has been situated under the context of real functions. In this work, we present two examples of variable exponent spaces of analytic functions: variable exponent Hardy spaces and variable exponent Bergman spaces. We will introduce the spaces together with some basic properties and the main techniques used in the context. We will show that in both cases, the boundedness of the evaluation functionals plays a key role in the theory. We also present a section of possible directions of research in this topic.

scholarly journals Interpolation by multipliers on certain spaces of analytic functions

2000 ◽  
Vol 23 (8) ◽  
pp. 547-554
Author(s):  
K. Mosaleheh ◽  
K. Seddighi
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Linear Functional ◽  
Dirichlet Space ◽  
Planar Domain ◽  
Space Of Analytic Functions ◽  
Spectral Set ◽  
Spaces Of Analytic Functions

Letℋbe a Hilbert space of analytic functions on a planar domainGsuch that, for eachλinG, the linear functionaleλof evaluation atλis bounded onℋ. Furthermore, assume thatzℋ⊂ℋandσ(Mz)=G¯is anM-spectral set forMz, the operator of multiplication byz. This paper is devoted to the study of interpolation by multipliers of the spaceℋand, in particular, the Dirichlet space.

Invariant subspaces of given index in Banach spaces of analytic functions

1998 ◽  
Vol 1998 (505) ◽  
pp. 23-44 ◽  
Author(s):  
Alexander Borichev
Keyword(s):  
Banach Spaces ◽  
Wide Class ◽  
Analytic Functions ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Invariant Subspaces ◽  
Weighted Bergman Spaces ◽  
Common Zeros ◽  
Spaces Of Analytic Functions

Abstract For a wide class of Banach spaces of analytic functions in the unit disc including all weighted Bergman spaces with radial weights and for weighted ℓAp spaces we construct z-invariant subspaces of index n, 2 ≦ n ≦ + ∞, without common zeros in the unit disc.

scholarly journals On New Decomposition Theorems in some Analytic Function Spaces in Bounded Pseudoconvex Domains

2020 ◽  
pp. 503-514
Author(s):  
Romi F. Shamoyan ◽  
Elena B. Tomashevskaya
Keyword(s):  
Analytic Function ◽  
Unit Ball ◽  
Analytic Functions ◽  
Atomic Decomposition ◽  
Smooth Boundary ◽  
Bergman Spaces ◽  
Pseudoconvex Domains ◽  
Decomposition Theorems ◽  
Analytic Function Spaces ◽  
Spaces Of Analytic Functions

We provide new sharp decomposition theorems for multifunctional Bergman spaces in the unit ball and bounded pseudoconvex domains with smooth boundary expanding known results from the unit ball. Namely we prove that mΠ j=1 jjfj jjXj ≍ jjf1 : : : fmjj Ap for various (Xj) spaces of analytic functions in bounded pseudoconvex domains with smooth boundary where f; fj ; j = 1; : : : ;m are analytic functions and where Ap ; 0 < p < 1; > �����1 is a Bergman space. This in particular also extend in various directions a known theorem on atomic decomposition of Bergman Ap spaces.

scholarly journals Multipliers on Spaces of Analytic Functions

1995 ◽  
Vol 47 (1) ◽  
pp. 44-64 ◽  
Author(s):  
Oscar Blasco
Keyword(s):  
Hardy Spaces ◽  
Analytic Functions ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Space Of Analytic Functions ◽  
Spaces Of Analytic Functions

AbstractIn the paper we find, for certain values of the parameters, the spaces of multipliers (H(p, q, α), H(s, t, β) and (H(p, q, α), ls), where H(p, q, α) denotes the space of analytic functions on the unit disc such that . As corollaries we recover some new results about multipliers on Bergman spaces and Hardy spaces.

scholarly journals Atomic decompositions in weighted Bergman spaces of analytic functions on strictly pseudoconvex domains

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2545-2563
Author(s):  
Milos Arsenovic
Keyword(s):  
Analytic Functions ◽  
Atomic Decomposition ◽  
Smooth Boundary ◽  
Bergman Spaces ◽  
Real Variable ◽  
Weighted Bergman Spaces ◽  
Pseudoconvex Domains ◽  
Atomic Decompositions ◽  
Strictly Pseudoconvex Domain ◽  
Spaces Of Analytic Functions

We construct an atomic decomposition of the weighted Bergman spaces Ap?(D) (0 < p ? 1, ? > -1) of analytic functions on a bounded strictly pseudoconvex domain D in Cn with smooth boundary. The atoms used are atoms in the real-variable sense.

On the Recovery of Analytic Functions

1996 ◽  
Vol 48 (2) ◽  
pp. 288-301
Author(s):  
Joseph A. Cima ◽  
Michael Stessin
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Analytic Functions ◽  
Bergman Spaces ◽  
Reproducing Kernels ◽  
Hardy And Bergman Spaces ◽  
The Given ◽  
Principal Method ◽  
Spaces Of Analytic Functions ◽  
Uniqueness Set

AbstractIn this paper we consider questions of recapturing an analytic function in a Banach space from its values on a uniqueness set. The principal method is to use reproducing kernels to construct a sequence in the Banach space which converges in norm to the given functions. The method works for several classical Banach spaces of analytic functions including some Hardy and Bergman spaces.

scholarly journals Norms of inclusions between some spaces of analytic functions

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Adrián Llinares
Keyword(s):  
Besov Spaces ◽  
Analytic Functions ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Spaces Of Analytic Functions

AbstractThe inclusions between the Besov spaces $$B^q$$ B q , the Bloch space $$\mathcal {B}$$ B and the standard weighted Bergman spaces $$A^p_{\alpha}$$ A α p are completely understood, but the norms of the corresponding inclusion operators are in general unknown. In this work, we compute or estimate asymptotically the norms of these inclusions.

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