Sharp fractional Hardy inequalities with a remainder for $1<p<2$
Bart{\l}omiej Dyda, Micha{\l} Kijaczko
TL;DR
This paper establishes new weighted fractional Hardy inequalities with remainders and Hardy-Sobolev-Maz'ya inequalities specifically for the range 1<p<2, advancing the understanding of fractional inequalities in this context.
Contribution
It introduces novel fractional Hardy inequalities with remainders and Hardy-Sobolev-Maz'ya inequalities for the case 1<p<2, filling a gap in the existing literature.
Findings
Derived weighted fractional Hardy inequalities with remainders.
Established fractional Hardy-Sobolev-Maz'ya inequalities for 1<p<2.
Extended the applicability of fractional inequalities to new parameter ranges.
Abstract
The main purpose of this article is to obtain (weighted) fractional Hardy inequalities with a remainder and fractional Hardy-Sobolev-Maz'ya inequalities valid for .
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems