Approach regions for L^p potentials with respect to the square root of the Poisson kernel
- Autores: M. Brundin
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 96, Nº 2, 2005, págs. 243-256
- Idioma: inglés
- DOI: 10.7146/math.scand.a-14955
- Enlaces
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Resumen
{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 (1≤p<∞) 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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