Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces

Walter Farkas, Niels Jacob, and René L. Schilling. Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces. 2001. <http://eudml.org/doc/286042>.

@book{WalterFarkas2001,
abstract = {We introduce and systematically investigate Bessel potential spaces associated with a real-valued continuous negative definite function. These spaces can be regarded as (higher order) $L_\{p\}$-variants of translation invariant Dirichlet spaces and in general they are not covered by known scales of function spaces. We give equivalent norm characterizations, determine the dual spaces and prove embedding theorems. Furthermore, complex interpolation spaces are calculated. Capacities are introduced and the existence of quasi-continuous modifications is shown.},
author = {Walter Farkas, Niels Jacob, René L. Schilling},
keywords = {anisotropic Bessel potential spaces; subordination in the sense of Bochner; potential theory; -capacities; interpolation of operators; Dirichlet spaces; convolution semigroup; sub-probability measures; submarkovian semigroup; infinitesimal generator; complex interpolation},
language = {eng},
title = {Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces},
url = {http://eudml.org/doc/286042},
year = {2001},
}

TY - BOOK
AU - Walter Farkas
AU - Niels Jacob
AU - René L. Schilling
TI - Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces
PY - 2001
AB - We introduce and systematically investigate Bessel potential spaces associated with a real-valued continuous negative definite function. These spaces can be regarded as (higher order) $L_{p}$-variants of translation invariant Dirichlet spaces and in general they are not covered by known scales of function spaces. We give equivalent norm characterizations, determine the dual spaces and prove embedding theorems. Furthermore, complex interpolation spaces are calculated. Capacities are introduced and the existence of quasi-continuous modifications is shown.
LA - eng
KW - anisotropic Bessel potential spaces; subordination in the sense of Bochner; potential theory; -capacities; interpolation of operators; Dirichlet spaces; convolution semigroup; sub-probability measures; submarkovian semigroup; infinitesimal generator; complex interpolation
UR - http://eudml.org/doc/286042
ER -