Exact constant in Sobolev's and Sobolev's trace inequalities for Grand Lebesgue Spaces

Abstract

In this article we generalize the classical Sobolev's and Sobolev's trace inequalities on the Grand Lebesgue Spaces instead the classical Lebesgue Spaces.We will distinguish the classical Sobolev's inequality and the so-called trace Sobolev's inequality.We consider for simplicity only the case of whole space.

Exact constant in Sobolev's and Sobolev's trace inequalities for Grand Lebesgue Spaces with monomial weight

“…The case A = B = 0 is provided in [39] by means of construction of corresponding example; the general case follows immediately from the main result of the article [40].…”