Espaces de fonctions à moyenne fractionnaire intégrable sur les groupes localement compacts

Details Espaces de fonctions à moyenne fractionnaire intégrable sur les groupes localement compacts Espaces de fonctions à moyenne fractionnaire intégrable sur les groupes localement compacts

2008-10-07

arxiv.org/abs/0810.1206v1

Afrika Matematika serie 3, volume 15, (2003) 73-91

Mathematics

Classical Analysis and ODEs

19 pages

Scientific paper

Let $G$ be a locally compact group which is $\sigma $-compact, endowed with a left Haar measure $\lambda .$ Denote by $e$ the unit element of $G$, and by $B$ an open relatively compact and symmetric neighbourhood of $e$. For every $(p,q) $ belonging to $[ 1 ; +\infty ] ^{2}$, we give an equivalent and a priori more manageable definition of the Banach space $L_{(q,p)}^{\pi}(G),$ defined by R. C. Busby and H. A. Smith in \cite% {1}. In the case $G$ is a group of homogeneous type, we look at the subspaces $(L^{q},L^{p}) ^{\alpha}(G)$ of the space $% L_{(q,p)}^{\pi}(G)$. Theses subspaces are extensions to non abelian groups of the spaces of functions with integrable mean, defined by I. Fofana in \cite{2}. Finally we show that $L^{\alpha ,+\infty}(G)$ is a complex subspace of $(L^{q},L^{p}) ^{\alpha}(G)$.

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