## A Banach principle for L1

- B-J A. Bellow, R. L. Jones
- Adv. Math
- 1996

- Published 1999

Approach regions for the square root of the Poisson kernel and weak L p boundary functions MARTIN BRUNDIN c Acknowledgement Peter Sjj ogren is an excellent advisor and teacher. His ability to bring about comprehension continues to fascinate me. I am grateful for his patience and, most of all, for his invaluable support. I also wish to thank the people at the Department of Mathematics, in particular Vilhelm Adolfsson and Peter Kumlin who have always been open to formal and informal discussions, mathematical or not. Special thanks also to Fausto Di Biase for having taken the time to read parts of my thesis and suggest improvements. Abstract. Let P 0 f(z) = R T p P (z;)f(e ii) dd for f 2 L 1 (T), where P (z;) is the Poisson kernel in the unit disc. In this paper we consider the convergence properties of the normalised operator P 0 f=P 0 1. We give a complete character-isation of the natural approach regions along which one has almost everywhere convergence for weak L p boundary functions, 1 < p < 1.

@inproceedings{Brundin1999THESISFT,
title={THESIS FOR THE DEGREE OF LICENTIATE OF PHILOSOPHY Approach regions for the square root of the Poisson kernel and weak Lp boundary functions},
author={Martin Brundin and Vilhelm Adolfsson},
year={1999}
}