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

M. Brundin

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 345-365
  • ISSN: 0011-4642

Abstract

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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 Φ having the property L ∞ ⊂ L Φ ⊂ L p , 1 ≤ p < ∞ . The second contains spaces L Φ that resemble L p spaces.

How to cite

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Brundin, M.. "Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces." Czechoslovak Mathematical Journal 57.1 (2007): 345-365. <http://eudml.org/doc/31133>.

@article{Brundin2007,
abstract = {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.},
author = {Brundin, M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {square root of the Poisson kernel; approach regions; almost everywhere convergence; maximal functions; Orlicz spaces; almost everywhere convergence; maximal functions; Orlicz spaces},
language = {eng},
number = {1},
pages = {345-365},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces},
url = {http://eudml.org/doc/31133},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Brundin, M.
TI - Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 345
EP - 365
AB - 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.
LA - eng
KW - square root of the Poisson kernel; approach regions; almost everywhere convergence; maximal functions; Orlicz spaces; almost everywhere convergence; maximal functions; Orlicz spaces
UR - http://eudml.org/doc/31133
ER -

References

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