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Images of some functions and functional spaces under the Dunkl-Hermite semigroup

Néjib Ben Salem, Walid Nefzi (2013)

Commentationes Mathematicae Universitatis Carolinae

We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, 𝒮 ( ) and L α p ( ) , 1 < p < , under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.

Imbedding theorems of Sobolev spaces into Lorentz spaces

Luc Tartar (1998)

Bollettino dell'Unione Matematica Italiana

In questo articolo vengono date alcune varianti del teorema di immersione di Sobolev in spazi di Lorentz. In particolare si dimostra un teorema di immersione per spazi di Sobolev anisotropi supponendo che le derivate parziali appartengono a spazi di Lorentz diversi, anche nel caso limite, corrispondente all’estensione di Brezis-Wainger del teorema di Trudinger per W 1 , N ( N ) .

Improved estimates for the Ginzburg-Landau equation : the elliptic case

Fabrice Bethuel, Giandomenico Orlandi, Didier Smets (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the G L -energy E ε and the parameter ε . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.

Indices of Orlicz spaces and some applications

Alberto Fiorenza, Miroslav Krbec (1997)

Commentationes Mathematicae Universitatis Carolinae

We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.

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