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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}.$
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R. A. Adams / 2003 / Sobolev Spaces / Academic Press :305
G. Anatriello / 2014 / Iterated grand and small Lebesgue spaces / Collect. Math 65:273~284
I. Aydin / 2009 / The inclusion Lp(x)( ) Lq(x)( ) / Int. J. Appl. Math 22(7):1031~1040
C. Capone / 2013 / Grand Lebesgue spaces with respect to measurable functions / Nonlinear Anal 85:125~131
H. Cartan / 1971 / Di erential Calculus / Hermann
G. Anatriello / 2014 / Iterated grand and small Lebesgue spaces / Collect. Math 65:273~284
I. Aydin / 2009 / The inclusion Lp(x)( ) Lq(x)( ) / Int. J. Appl. Math 22(7):1031~1040
C. Capone / 2013 / Grand Lebesgue spaces with respect to measurable functions / Nonlinear Anal 85:125~131
H. Cartan / 1971 / Di erential Calculus / Hermann
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