Hardy spaces for the Laplacian with lower order perturbations

Tomasz Luks¹

¹ LAREMA Laboratoire de Mathématiques Université d'Angers 2 bd. Lavoisier 49045 Angers, France

Studia Mathematica, Tome 204 (2011) no. 1, pp. 39-62

Résumé

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.

Détail

DOI : 10.4064/sm204-1-3

Keywords: consider hardy spaces functions harmonic smooth domains euclidean spaces dimension greater respect laplacian perturbed lower order terms gradient schr dinger perturbations under appropriate kato conditions context usual correspondence between harmonic hardy spaces spaces space finite measures boundary end prove uniform comparability respective harmonic measures class approximating domains relative fatou theorem harmonic functions perturbed operator