scholarly journals On the exact value of the norm of the Hilbert matrix operator on weighted Bergman spaces

2021 ◽  
Vol 46 (1) ◽  
pp. 201-224
Author(s):  
Mikael Lindström ◽  
Santeri Miihkinen ◽  
Niklas Wikman
Keyword(s):  
Bergman Spaces ◽  
Matrix Operator ◽  
Weighted Bergman Spaces ◽  
Hilbert Matrix

NORM OF THE HILBERT MATRIX OPERATOR ON THE WEIGHTED BERGMAN SPACES

2017 ◽  
Vol 60 (3) ◽  
pp. 513-525 ◽  
Author(s):  
BOBAN KARAPETROVIĆ
Keyword(s):  
Lower Bound ◽  
Bergman Space ◽  
Upper Bound ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Matrix Operator ◽  
Weighted Bergman Spaces ◽  
Formula Group ◽  
Hilbert Matrix ◽  
Image Position

AbstractWe find the lower bound for the norm of the Hilbert matrix operator H on the weighted Bergman space Ap,α \begin{equation*} \|H\|_{A^{p,\alpha}\rightarrow A^{p,\alpha}}\geq\frac{\pi}{\sin{\frac{(\alpha+2)\pi}{p}}}, \,\, \textnormal{for} \,\, 1<\alpha+2<p. \end{equation*} We show that if 4 ≤ 2(α + 2) ≤ p, then ∥H∥Ap,α → Ap,α = $\frac{\pi}{\sin{\frac{(\alpha+2)\pi}{p}}}$, while if 2 ≤ α +2 < p < 2(α+2), upper bound for the norm ∥H∥Ap,α → Ap,α, better then known, is obtained.

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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