Traces on JW-Algebras and Enveloping W*-Algebras.
The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces. This can be expressed in terms of tractability envelopes.
The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces.
We show that the transference method of Coifman and Weiss can be extended to Hardy and Sobolev spaces. As an application we obtain the de Leeuw restriction theorems for multipliers.
Certain weighted norm inequalities for integral operators with non-negative, monotone kernels are shown to remain valid when the weight is replaced by a monotone majorant or minorant of the original weight. A similar result holds for operators with quasi-concave kernels. To prove these results a careful investigation of the functional properties of the monotone envelopes of a non-negative function is carried-out. Applications are made to function space embeddings of the cones of monotone functions...
Nous étudions d’abord la transformation de Fourier sur les espaces qui sont formés de fonctions appartenant localement à et se comportant à l’infini comme des éléments de . Si , les transformées de Fourier des éléments de appartiennent à . Dans les autres cas, nous donnons quelques résultats partiels.Nous montrons ensuite que est le plus grand espace vectoriel solide de fonctions mesurables sur lequel la transformation de Fourier puisse se définir par prolongement par continuité.