Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure
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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.
2015 ◽
Vol 83
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pp. 413-428
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2000 ◽
Vol 42
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pp. 31-35
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1985 ◽
Vol 26
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pp. 13-17
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1996 ◽
Vol 48
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pp. 930-945
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2014 ◽
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pp. 129-132
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2019 ◽
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pp. 106-117
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1989 ◽
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pp. 265-276
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