Strong-Type Inequality for Convolution with Square Root of the Poisson Kernel

被引：0
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作者：
I. N. Katkovskaya
V. G. Krotov
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来源：
Mathematical Notes | 2004年 / 75卷
关键词：
convolution with square root of the Poisson kernel; Poisson kernel; maximal operator; compact Hausdorff space; Borel measure;
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摘要：
The boundary behavior of convolutions with Poisson kernel and with square root of the Poisson kernel is essentially different. The former has only a nontangential limit. The latter involves convergence over domains admitting the logarithmic order of tangency with the boundary (P. Sjögren, J.-O. Rönning). This result was generalized by the authors to spaces of homogeneous type. Here we prove the boundedness in Lp, p > 1, of the corresponding maximal operator. Only a weak-type inequality was known before.
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页码：542 / 552
页数：10
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