Radial Operators on the Weighted Bergman Spaces over the Polydisk

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.

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Sums of weighted differentiation composition operators from weighted Bergman spaces to weighted Zygmund and Bloch-type spaces

Advances in Operator Theory ◽

10.1007/s43036-021-00147-0 ◽

2021 ◽

Vol 6 (3) ◽

Author(s):

Jasbir S. Manhas ◽

Mohammed S. Al Ghafri

Keyword(s):

Composition Operators ◽

Bergman Spaces ◽

Weighted Bergman Spaces ◽

Type Spaces

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Eigenvalues of K-invariant Toeplitz Operators on Bounded Symmetric Domains

Integral Equations and Operator Theory ◽

10.1007/s00020-021-02639-3 ◽

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 ) .

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Reproducing Kernels of Some Weighted Bergman Spaces

Journal of Geometric Analysis ◽

10.1007/s12220-021-00616-1 ◽

2021 ◽

Author(s):

Guan-Tie Deng ◽

Yun Huang ◽

Tao Qian

Keyword(s):

Bergman Spaces ◽

Reproducing Kernels ◽

Weighted Bergman Spaces

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The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

Potential Analysis ◽

10.1007/s11118-021-09915-2 ◽

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.

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