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Hardy spaces for the Laplacian with lower order perturbations

Tomasz Luks (2011)

Studia Mathematica

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...

Heat kernel of fractional Laplacian in cones

Krzysztof Bogdan, Tomasz Grzywny (2010)

Colloquium Mathematicae

We give sharp estimates for the transition density of the isotropic stable Lévy process killed when leaving a right circular cone.

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