Throughout this section E will be a locally compact separable metric space equipped with its
Borel-algebra BE/. We write MC. E/for the set of all locally finite, inner regular Borel …

Characterisations of function spaces of generalised smoothness Page 1 Digital Object
Identifier (DOI) 10.1007/s10231-004-0110-z Annali di Matematica 185, 1–62 (2006) Walter …

We prove necessary and sufficient conditions for the existence of (smooth) transition
probability densities for Lévy processes and isotropic Lévy processes. Under some mild …

The paper gives a detailed survey of recent results on elliptic problems in Hilbert spaces of
generalized smoothness. The latter are the isotropic Hörmander spaces $ H^{s,\varphi}:= B …

We study Fourier multipliers which result from modulating jumps of Lévy processes. Using
the theory of martingale transforms we prove that these operators are bounded in Lp (Rd) for …

In this paper, we present an-regularity theory for parabolic equations of the form Here,
represents anisotropic nonlocal operators encompassing the singular anisotropic fractional …

By using Fourier's transform and Fefferman–Stein's theorem, we investigate the Lp-maximal
regularity of nonlocal parabolic and elliptic equations with singular and non-symmetric Lévy …

Optimal Hardy inequality for the fractional Laplacian on Lp - ScienceDirect Skip to main
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In this article, the authors study the Lebesgue point of functions from Hajłasz–Sobolev,
Besov, and Triebel–Lizorkin spaces with generalized smoothness on doubling metric …

The question of extending Lp-sub-Markovian semigroups to the spaces Lq, q> p, and the
interpolation of Lp-sub-Markovian semigroups with Feller semigroups is investigated. The …