scholarly journals Area integral means, Hardy and weighted Bergman spaces of planar harmonic mappings

2013 ◽  
Vol 36 (2) ◽  
pp. 313-324 ◽  
Author(s):  
Shaolin Chen ◽  
Saminathan Ponnusamy ◽  
Xiantao Wang
Keyword(s):  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Harmonic Mappings ◽  
Integral Means ◽  
Area Integral ◽  
Planar Harmonic Mappings

scholarly journals Addendum to the Paper “A note on Weighted bergman Spaces and the cesaro operator”

2005 ◽  
Vol 180 ◽  
pp. 77-90 ◽  
Author(s):  
Der-Chen Chang ◽  
Stevo Stević
Keyword(s):  
Bergman Space ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Cesàro Operator ◽  
Integral Means ◽  
Measurable Functions ◽  
Unit Polydisk ◽  
Cesaro Operator

AbstractLet H(Dn) be the space of holomorphic functions on the unit polydisk Dn, and let , where p, q> 0, α = (α1,…,αn) with αj > -1, j =1,..., n, be the class of all measurable functions f defined on Dn such thatwhere Mp(f,r) denote the p-integral means of the function f. Denote the weighted Bergman space on . We provide a characterization for a function f being in . Using the characterization we prove the following result: Let p> 1, then the Cesàro operator is bounded on the space .

Hadamard Convolution and Area Integral Means in Bergman Spaces

2020 ◽  
Vol 75 (2) ◽  
Author(s):  
Boban Karapetrović ◽  
Javad Mashreghi
Keyword(s):  
Bergman Spaces ◽  
Integral Means ◽  
Area Integral

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 ) .

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