Hardy spaces for the Laplacian with lower order perturbations

• Autorzy: Tomasz Luks
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 31B25: Boundary behavior
• 60J45: Probabilistic potential theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 204
• Numer: 1
• Strony: 39-62

Daty

wydano

2011

Twórcy

autor

Tomasz Luks

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

Identyfikatory

DOI

10.4064/sm204-1-3