On Dirichlet Spaces With a Class of Superharmonic Weights
2018 ◽
Vol 70
(4)
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pp. 721-741
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Keyword(s):
AbstractIn this paper, we investigate Dirichlet spaces with superharmonic weights induced by positive Borel measures μ on the open unit disk. We establish the Alexander-Taylor-Ullman inequality for spaces and we characterize the cases where equality occurs. We define a class of weighted Hardy spaces via the balayage of the measure μ. We show that is equal to if and only if μ is a Carleson measure for . As an application, we obtain the reproducing kernel of when μ is an infinite sum of point-mass measures. We consider the boundary behavior and innerouter factorization of functions in . We also characterize the boundedness and compactness of composition operators on .
2012 ◽
Vol 2012
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pp. 1-20
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2006 ◽
Vol 13
(4)
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pp. 739-742
1986 ◽
Vol 38
(4)
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pp. 878-906
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2012 ◽
Vol 218
(17)
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pp. 8347-8352
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1992 ◽
Vol 44
(6)
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pp. 1206-1219
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2014 ◽
Vol 66
(6)
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pp. 1382-1412
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