- Turkish Journal of Mathematics
- Vol: 40 Issue: 3
- The inclusion theorems for variable exponent Lorentz spaces
The inclusion theorems for variable exponent Lorentz spaces
Authors : Öznur Kulak
Pages : 605-619
View : 5 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Let $\left( \text{X,}\Sigma ,\mu \right) $ and $\left( \text{X,}\Sigma ,\nu \right) $ be measure spaces. Assume that $L^{p_{1}\left( .\right) ,q_{1}\left( .\right) }\left( X,\mu \right) $ and $L^{p_{2}\left( .\right) ,q_{2}\left( .\right) }\left( X,\nu \right) $ are two variable exponent Lorentz spaces where $p,q\in P_{0}\left( \left[ 0,l\right] \right) $. In this paper we investigated the existence of the inclusion $L^{p_{1}\left( .\right) ,q_{1}\left( .\right) }\left( X,\mu \right) $ $\subset L^{p_{2}\left( .\right) ,q_{2}\left( .\right) }\left( X,\nu \right) $ under what conditions for two measures $\mu $ and $\nu $ on $\left( X,\Sigma \right) .$Keywords : Inclusion, variable exponent Lorentz space