Abstract
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 L p, p > 1, of the corresponding maximal operator. Only a weak-type inequality was known before.
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