Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1174.42315
Brundin, M.
Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces. (English)
[J] Czech. Math. J. 57, No. 1, 345-365 (2007). ISSN 0011-4642; ISSN 1572-9141/e

Summary: 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 {\it J.-O.\,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\leq p<\infty $. The second contains spaces~ $L^{\Phi }$ that resemble $L^{p}$~ spaces.

MSC 2000:: *42B25 Maximal functions
42A99 Fourier analysis in one variable
43A85 Analysis on homogeneous spaces

Keywords: almost everywhere convergence; maximal functions; Orlicz spaces

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]