@article {
author = {Saiedinezhad, Somayeh},
title = {Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {7},
number = {2},
pages = {29-38},
year = {2016},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2016.439},
abstract = {Some functional inequalities in variable exponent Lebesgue spaces are presented. The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non- increasing function which is$$int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleqCint_0^infty f(x)^{p(x)}u(x)dx,$$ is studied. We show that the exponent $p(.)$ for which these modular inequalities hold must have constant oscillation. Also we study the boundedness of integral operator $Tf(x)=int K(x,y) f(x)dy$ on $L^{p(.)}$ when the variable exponent $p(.)$ satisfies some uniform continuity condition that is named $beta$-controller condition and so multiple interesting results which can be seen as a generalization of the same classical results in the constant exponent case, derived.},
keywords = {Hardy type inequality,Variable exponent Lebesgue space,Modular type inequality.},
url = {https://ijnaa.semnan.ac.ir/article_439.html},
eprint = {https://ijnaa.semnan.ac.ir/article_439_a9ff1b7775e024c726cd0418c812bd7b.pdf}
}