Self-improvement of weighted pointwise inequalities on open sets
Eriksson-Bique, Sylvester; Lehrbäck, Juha; Vähäkangas, Antti V. (2020). Self-improvement of weighted pointwise inequalities on open sets. Journal of Functional Analysis, 279, 108691. DOI: 10.1016/j.jfa.2020.108691 http://dx.doi.org/10.1016/j.jfa.2020.108691
Published inJournal of Functional Analysis
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We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of p-Poincaré and p-Hardy weights for an open set Ω⊂X, where X is a metric measure space. We also apply the self-improvement of weighted pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.