Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
عنوان مقاله: Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
شناسه ملی مقاله: JR_IJNAA-7-2_002
منتشر شده در در سال 1395
شناسه ملی مقاله: JR_IJNAA-7-2_002
منتشر شده در در سال 1395
مشخصات نویسندگان مقاله:
- - - Assistant professor of Iran University of Science and technology
خلاصه مقاله:
- - - Assistant professor of Iran University of Science and technology
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 isint_۰^infty (frac{۱}{x}int_۰^x f(t)dt)^{p(x)}v(x)dxleqCint_۰^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.
کلمات کلیدی: Hardy type inequality, Variable exponent Lebesgue space, Modular type inequality.
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1561903/