Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 2، دوره 7، شماره 2، 2016، صفحه 29-38 اصل مقاله (375.71 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2016.439 | ||
| نویسنده | ||
| Somayeh Saiedinezhad | ||
| Assistant professor of Iran University of Science and technology | ||
| چکیده | ||
| 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 $$ int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq Cint_0^infty f(x)^{p(x)}u(x)dx, $$ 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. | ||
| کلیدواژهها | ||
| Hardy type inequality؛ Variable exponent Lebesgue space؛ Modular type inequality. | ||
|
آمار تعداد مشاهده مقاله: 47,470 تعداد دریافت فایل اصل مقاله: 62,558 |
||
| تعداد نشریات | 22 |
| تعداد شمارهها | 718 |
| تعداد مقالات | 10,319 |
| تعداد مشاهده مقاله | 72,327,567 |
| تعداد دریافت فایل اصل مقاله | 64,054,186 |