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arXiv · 2101.05660

A note on $\sigma$-point and nontangential convergence

Jayanta Sarkar
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Abstract

In this article, we generalize a theorem of Victor L. Shapiro concerning nontangential convergence of the Poisson integral of a $L^p$-function. We introduce the notion of $\sigma$-points of a locally finite measure and consider a wide class of convolution kernels. We show that convolution integrals of a measure have nontangential limits at $\sigma$-points of the measure. We also investigate the relationship between $\sigma$-point and the notion of the strong derivative introduced by Ramey and Ullrich. In one dimension, these two notions are the same.

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Jayanta Sarkar. 2021-01-14. A note on $\sigma$-point and nontangential convergence. https://arxiv.org/abs/2101.05660

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