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.

scholarly journals Multiplicative Isometries and Isometric Zero-Divisors

2010 ◽  
Vol 62 (5) ◽  
pp. 961-974 ◽  
Author(s):  
Alexandru Aleman ◽  
Peter Duren ◽  
María J. Martín ◽  
Dragan Vukotić
Keyword(s):  
Banach Spaces ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Zero Divisors ◽  
Pointwise Multipliers ◽  
Type Spaces ◽  
Dirichlet Type Spaces ◽  
Coefficient Multipliers ◽  
Spaces Of Analytic Functions

AbstractFor some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.

scholarly journals The Bloch space and Besov spaces of analytic functions

1996 ◽  
Vol 54 (2) ◽  
pp. 211-219 ◽  
Author(s):  
Karel Stroethoff
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Besov Spaces ◽  
Analytic Functions ◽  
Elementary Proof ◽  
Bloch Space ◽  
Little Bloch Space ◽  
Spaces Of Analytic Functions

We shall give an elementary proof of a characterisation for the Bloch space due to Holland and Walsh, and obtain analogous characterisations for the little Bloch space and Besov spaces of analytic functions on the unit disk in the complex plane.

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 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.

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.

POWERS OF COMPOSITION OPERATORS: ASYMPTOTIC BEHAVIOUR ON BERGMAN, DIRICHLET AND BLOCH SPACES

2019 ◽  
Vol 108 (3) ◽  
pp. 289-320 ◽  
Author(s):  
W. ARENDT ◽  
I. CHALENDAR ◽  
M. KUMAR ◽  
S. SRIVASTAVA
Keyword(s):  
Asymptotic Behaviour ◽  
Banach Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Dirichlet Space ◽  
Complete Characterization ◽  
Weighted Bergman Spaces ◽  
Bloch Type Space ◽  
Spaces Of Holomorphic Functions

We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.

Sign in / Sign up

Export Citation Format

Share Document