The inclusion theorems for generalized variable exponent grand Lebesgue spaces

Abstract

In this paper, we discuss and investigate the existence of the inclusion $ L^{p(.),\theta }\left( \mu \right) \subseteq L^{q(.),\theta }\left( \nu \right) $, where $\mu $ and $\nu $ are two finite measures on $\left( X,\Sigma \right) .$ Moreover, we show that the generalized variable exponent grand Lebesgue space$ L^{p(.),\theta }\left( \Omega \right) $ has a potential-type approximate identity, where $\Omega $ is a bounded open subset of $ \mathbb{R}^{d}.$