Korean J. Math.  Vol 29, No 3 (2021)  pp.581-591
DOI: https://doi.org/10.11568/kjm.2021.29.3.581

The inclusion theorems for generalized variable exponent grand Lebesgue spaces

Ismail Aydin, Cihan Unal

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}.$


Keywords


Generalized variable exponent grand Lebesgue spaces, Inclusion, Approximate identity

Subject classification

43A15, 46E30

Sponsor(s)



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