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

2013/01/01 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #math.FA

paper · pdf · doi:10.48550/arxiv.1301.0132

arxiv created 2013/01/01 · openalex publication_date 2013/01/01 · arxiv updated 2013/01/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Module of continuity for the functions belonging to the Sobolev-Grand Lebesgue Spaces
• Hitchhiker's guide to the fractional Sobolev spaces

Cited by

• Central Limit Theorem in Holder spaces in the terms of majorizing measures

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