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- Title
Approach regions for the square root of the Poisson kernel and bounded functions.
- Authors
Sjögren, P.
- Abstract
If the Poisson kernel of the unit disc is replaced by its square root, it is known that normalised Poisson integrals of Lp boundary functions converge almost everywhere at the boundary, along approach regions wider than the ordinary non-tangential cones. The sharp approach region, defined by means of a monotone function, increases with p. We make this picture complete by determining along which approach regions one has almost everywhere convergence for L∞ boundary functions.
- Publication
Bulletin of the Australian Mathematical Society, 1997, Vol 55, Issue 3, p521
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972700034183