A note about extension of functions belonging to Sobolev-Grand Lebesgue Spaces

TL;DR

This paper establishes an extension theorem for Sobolev-Grand Lebesgue Spaces in finite-dimensional Euclidean spaces and provides estimates for the norms of the linear extension operator.

Contribution

It introduces a new extension theorem specific to Sobolev-Grand Lebesgue Spaces and estimates the associated linear extension operator norms.

Findings

Extension theorem for Sobolev-Grand Lebesgue Spaces

Norm estimates for the extension operator

Linear extension operator constructed and analyzed

Abstract

We deduce an extension theorem for the so-called Sobolev-Grand Lebesgue Spaces defined on the suitable subsets of the whole finite-dimensional Euclidean space, and estimate the norms of correspondent extension operator, which may be choosed as linear.