Approach regions for lp 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 Lp boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning (1p<) and Sjögren (p=1 and p=). In this paper we present new and simplified proofs of these results. We also generalise the L result to higher dimensions.

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Published

2005-06-01

How to Cite

Brundin, M. (2005). Approach regions for lp 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