Embedding theorems and integration operators on Bergman spaces with exponential weights

2019 ◽  
Vol 10 (1) ◽  
pp. 122-134
Author(s):  
Xiaofen Lv
Keyword(s):  
Bergman Spaces ◽  
Embedding Theorems ◽  
Exponential Weights

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 Embedding theorems for Bergman spaces via harmonic analysis

2014 ◽  
Vol 362 (1-2) ◽  
pp. 205-239 ◽  
Author(s):  
José Ángel Peláez ◽  
Jouni Rättyä
Keyword(s):  
Harmonic Analysis ◽  
Bergman Spaces ◽  
Embedding Theorems

scholarly journals Lipschitz Type Characterizations for Bergman Spaces

2009 ◽  
Vol 52 (4) ◽  
pp. 613-626 ◽  
Author(s):  
Hasi Wulan ◽  
Kehe Zhu
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Bergman Spaces ◽  
Embedding Theorems ◽  
Hyperbolic Metrics

AbstractWe obtain new characterizations for Bergman spaces with standard weights in terms of Lipschitz type conditions in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As a consequence, we prove optimal embedding theorems when an analytic function on the unit disk is symmetrically lifted to the bidisk.

Bergman spaces with exponential weights

2019 ◽  
Vol 276 (5) ◽  
pp. 1402-1429 ◽  
Author(s):  
Zhangjian Hu ◽  
Xiaofen Lv ◽  
Alexander P. Schuster
Keyword(s):  
Bergman Spaces ◽  
Exponential Weights
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