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Zbl 0903.31002
Sjögren, P.
Approach regions for the square root of the Poisson kernel and bounded functions.
(English)
[J] Bull. Aust. Math. Soc. 55, No.3, 521-527 (1997). ISSN 0004-9727

Summary: If the Poisson kernel of the unit disc is replaced by its square root, it is known that normalized Poisson integrals of $L^p$ boundary functions converge almost everywhere at the boundary, along approach regions wider than the ordinary nontangential 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 $L^\infty$ boundary functions.
MSC 2000:
*31A20 Boundary behavior of harmonic functions (two-dim.)
42B25 Maximal functions
43A85 Analysis on homogeneous spaces

Keywords: Poisson kernel; Poisson integrals; $L^p$ boundary functions; approach regions; almost everywhere convergence

Cited in: Zbl 1085.31001 Zbl 1075.31004

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