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

Abstract

In this short article we generalize the Sobolev's inequalities for the module of continuity for the functions belonging to the classical Lebesgue space on the (Bilateral) Grand Lebesgue spaces. We construct also some examples in order to show the exactness of obtained results.

References in corpus (3)

• Riesz's and Bessel's Operators in Bilateral Grand Lebesgue Spaces
• Nikol'skii-type inequalities for rearrangement invariant spaces
• Bide - Side Exponential and Moment Inequalities for Tails of Distributions of Polynomial Martingales

Cited by in corpus (7)

• CLT for continuous random processes under approximations terms
• Continuity of functions belonging to the fractional order Sobolev-Grand Lebesgue Spaces
• Central Limit Theorem in Holder spaces in the terms of majorizing measures
• Theory of approximation and continuity of random processes
• Uniform measures on the arbitrary compact metric spaces, with applications
• Exact constant in Sobolev's and Sobolev's trace inequalities for Grand Lebesgue Spaces with monomial weight
• Poincare type inequalities for two different Bilateral Grand Lebesgue Spaces