Approach regions for $l^{p}$ potentials with respect to the square root of the Poisson kernel

Authors

  • Martin Brundin

DOI:

https://doi.org/10.7146/math.scand.a-14955

Abstract

{If} one replaces the Poisson kernel of the unit disc by its square root, then normalised Poisson integrals of $L^{p}$ boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning ($1\leq p<\infty$) and Sjögren ($p=1$ and $p=\infty$). In this paper we present new and simplified proofs of these results. We also generalise the $L^{\infty}$ result to higher dimensions.

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Published

2005-06-01

How to Cite

Brundin, M. (2005). Approach regions for $l^{p}$ potentials with respect to the square root of the Poisson kernel. MATHEMATICA SCANDINAVICA, 96(2), 243–256. https://doi.org/10.7146/math.scand.a-14955

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Section

Articles