Fractional Poincaré and localized Hardy inequalities on metric spaces

Abstract

We prove fractional Sobolev-Poincaré inequalities, capacitary versions of fractional Poincaré inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results generalize and extend earlier work where such inequalities have been considered in the Euclidean spaces or in the non-fractional setting in metric spaces. The results concerning pointwise and localized variants of fractional Hardy inequalities are new even in the Euclidean case.

Cited by in corpus (1)

• Characterization of fractional Sobolev--Poincaré and (localized) Hardy inequalities