On Scales of Sobolev spaces associated to generalized Hardy operators

Abstract

We consider the fractional Laplacian with Hardy potential and study the scale of homogeneous $L^p$ Sobolev spaces generated by this operator. Besides generalized and reversed Hardy inequalities, the analysis relies on a Hörmander multiplier theorem which is crucial to construct a basic Littlewood--Paley theory. The results extend those obtained recently in $L^2$ but do not cover negative coupling constants in general due to the slow decay of the associated heat kernel.

Corrected some misprints. This is a pre-print of an article published in Mathematische Zeitschrift, available online at https://doi.org/10.1007/s00209-020-02651-0

References in corpus (1)

• Equivalence of Sobolev norms involving generalized Hardy operators

Cited by in corpus (3)

• On Sobolev norms involving Hardy operators in a half-space
• Ground state representation for the fractional Laplacian with Hardy potential in angular momentum channels
• On complex-time heat kernels of fractional Schrödinger operators via Phragmén-Lindelöf principle