期刊
ADVANCES IN DIFFERENCE EQUATIONS
卷 2021, 期 1, 页码 -出版社
SPRINGER
DOI: 10.1186/s13662-021-03552-0
关键词
Reverse Holder's inequality; Muckenhoupt type inequality; Reverse Holder's inequality; Higher integrability; Gehring type inequalities
资金
- Prince Sultan University
- OSTIM Technical University
This paper proves the self-improving property of the weighted Gehring class in non-homogeneous spaces, obtaining sharp bounds of exponents and applying it to the self-improving property of the Muckenhoupt class. By utilizing rearrangement of functions and Jensen inequality, the results cover non-monotonic functions and provide a higher integrability theorem. Furthermore, solutions of partial differential equations can be solved in an extended space using this self-improving property, reflecting a different approach to inequalities of Hardy type.
In this paper, we prove that the self-improving property of the weighted Gehring class G(lambda)(p). with a weight lambda holds in the non-homogeneous spaces. The results give sharp bounds of exponents and will be used to obtain the self-improving property of the Muckenhoupt class A(q). By using the rearrangement (nonincreasing rearrangement) of the functions and applying the Jensen inequality, we show that the results cover the cases of non-monotonic functions. For applications, we prove a higher integrability theorem and report that the solutions of partial differential equations can be solved in an extended space by using the self-improving property. Our approach in this paper is different from the ones used before and is based on proving some new inequalities of Hardy type designed for this purpose.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据