Discretizations of Integral Operators and Atomic Decompositions in Vector-Valued Weighted Bergman Spaces

2007 ◽  
Vol 59 (4) ◽  
pp. 523-554 ◽  
Author(s):  
Olivia Constantin
Keyword(s):  
Bergman Spaces ◽  
Integral Operators ◽  
Weighted Bergman Spaces ◽  
Atomic Decompositions ◽  
Vector Valued

scholarly journals Schatten-von Neumann properties of bilinear Hankel forms of higher weights

2006 ◽  
Vol 98 (2) ◽  
pp. 283
Author(s):  
Marcus Sundhäll
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Besov Spaces ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Von Neumann ◽  
Higher Weights ◽  
Vector Valued

Hankel forms of higher weights, on weighted Bergman spaces in the unit ball of $\mathsf{C}^d$, were introduced by Peetre. Each Hankel form corresponds to a vector-valued holomorphic function, called the symbol of the form. In this paper we characterize bounded, compact and Schatten-von Neumann $\mathcal{S}_p$ class ($2\leq p<\infty$) Hankel forms in terms of the membership of the symbols in certain Besov 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.

scholarly journals Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Changbao Pang ◽  
Antti Perälä ◽  
Maofa Wang
Keyword(s):  
Borel Measure ◽  
Bergman Spaces ◽  
Embedding Theorem ◽  
Weighted Bergman Spaces ◽  
Embedding Theorems ◽  
Positive Borel Measure ◽  
Doubling Property ◽  
Area Operator ◽  
Special Cases ◽  
Upper Half Plane

AbstractWe establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$ d ω ( y ) d x with the doubling property $$\omega (0,2t)\le C\omega (0,t)$$ ω ( 0 , 2 t ) ≤ C ω ( 0 , t ) . The characterization is given in terms of Carleson squares on the upper half-plane. As special cases, our result covers the standard weights and logarithmic weights. As an application, we also establish the boundedness of the area operator.

scholarly journals Eigenvalues of K-invariant Toeplitz Operators on Bounded Symmetric Domains

2021 ◽  
Vol 93 (3) ◽  
Author(s):  
Harald Upmeier
Keyword(s):  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Bounded Symmetric Domains

AbstractWe determine the eigenvalues of certain “fundamental” K-invariant Toeplitz type operators on weighted Bergman spaces over bounded symmetric domains $$D=G/K,$$ D = G / K , for the irreducible K-types indexed by all partitions of length $$r={\mathrm {rank}}(D)$$ r = rank ( D ) .

scholarly journals The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

2021 ◽  
Author(s):  
Cezhong Tong ◽  
Junfeng Li ◽  
Hicham Arroussi
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Kernel Estimates ◽  
Berezin Transforms

AbstractIn this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.

Intersections and Unions of Weighted Bergman Spaces

2006 ◽  
Vol 5 (2) ◽  
pp. 459-469 ◽  
Author(s):  
Risto Korhonen ◽  
Jouni Rättyä
Keyword(s):  
Bergman Spaces ◽  
Weighted Bergman Spaces
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