Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces

Title:

Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces

Creator:

Brundin, M.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:48ac2ad9-ee16-40f0-b197-b314c44698a8
uuid:48ac2ad9-ee16-40f0-b197-b314c44698a8

Subject:

square root of the Poisson kernel, approach regions, almost everywhere convergence, maximal functions, and Orlicz spaces

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

If the Poisson integral of the unit disc is replaced by its square root, it is known that normalized Poisson integrals of $L^{p}$ and weak $L^{p}$ boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning and the author, respectively. In this paper we characterize the approach regions for boundary functions in two general classes of Orlicz spaces. The first of these classes contains spaces $L^{\Phi }$ having the property $L^{\infty }\subset L^{\Phi }\subset L^{p}$, $1\le p<\infty $. The second contains spaces $L^{\Phi }$ that resemble $L^{p}$ spaces.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

345-365

Source:

Czechoslovak Mathematical Journal | 2007 Volume:57 | Number:1

Harvested from:

CDK

Metadata only:

false