Hardy spaces for the Laplacian with lower order perturbations

Tomasz Luks. "Hardy spaces for the Laplacian with lower order perturbations." Studia Mathematica 204.1 (2011): 39-62. <http://eudml.org/doc/285562>.

@article{TomaszLuks2011,
abstract = {We consider Hardy spaces of functions harmonic on smooth domains in Euclidean spaces of dimension greater than two with respect to the Laplacian perturbed by lower order terms. We deal with the gradient and Schrödinger perturbations under appropriate Kato conditions. In this context we show the usual correspondence between the harmonic Hardy spaces and the $L^\{p\}$ spaces (or the space of finite measures if p = 1) on the boundary. To this end we prove the uniform comparability of the respective harmonic measures for a class of approximating domains and the relative Fatou theorem for harmonic functions of the perturbed operator.},
author = {Tomasz Luks},
journal = {Studia Mathematica},
keywords = {Hardy spaces; diffusion operators; harmonic functions},
language = {eng},
number = {1},
pages = {39-62},
title = {Hardy spaces for the Laplacian with lower order perturbations},
url = {http://eudml.org/doc/285562},
volume = {204},
year = {2011},
}

TY - JOUR
AU - Tomasz Luks
TI - Hardy spaces for the Laplacian with lower order perturbations
JO - Studia Mathematica
PY - 2011
VL - 204
IS - 1
SP - 39
EP - 62
AB - We consider Hardy spaces of functions harmonic on smooth domains in Euclidean spaces of dimension greater than two with respect to the Laplacian perturbed by lower order terms. We deal with the gradient and Schrödinger perturbations under appropriate Kato conditions. In this context we show the usual correspondence between the harmonic Hardy spaces and the $L^{p}$ spaces (or the space of finite measures if p = 1) on the boundary. To this end we prove the uniform comparability of the respective harmonic measures for a class of approximating domains and the relative Fatou theorem for harmonic functions of the perturbed operator.
LA - eng
KW - Hardy spaces; diffusion operators; harmonic functions
UR - http://eudml.org/doc/285562
ER -