Continuity of functions belonging to the fractional order Sobolev-Grand Lebesgue Spaces

Abstract

We extend in this article the classical Sobolev inequalities for the module of continuity for the functions belonging to the integer order Sobolev's space on the Sobolev-Bilateral Grand Lebesgue spaces. As a consequence, we deduce the fractional Orlicz-Sobolev imbedding theorems and investigate the rectangle module of continuity of non-Gaussian multiparameter random fields.

References in corpus (1)

• Module of continuity for the functions belonging to the Sobolev-Grand Lebesgue Spaces

Cited by in corpus (6)

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• Central Limit Theorem in Holder spaces in the terms of majorizing measures
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• Exact constant in Sobolev's and Sobolev's trace inequalities for Grand Lebesgue Spaces with monomial weight