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Self-improving properties of weighted Gehring classes with applications to partial differential equations.
- Source :
-
Advances in Difference Equations . 8/26/2021, Vol. 2021 Issue 1, p1-20. 20p. - Publication Year :
- 2021
-
Abstract
- In this paper, we prove that the self-improving property of the weighted Gehring class G λ p with a weight λ 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *JENSEN'S inequality
*WEIGHTED graphs
Subjects
Details
- Language :
- English
- ISSN :
- 16871839
- Volume :
- 2021
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Difference Equations
- Publication Type :
- Academic Journal
- Accession number :
- 152105733
- Full Text :
- https://doi.org/10.1186/s13662-021-03552-0