On Scales of Sobolev spaces associated to generalized Hardy operators

Konstantin Merz

doi:10.1007/s00209-020-02651-0

On Scales of Sobolev spaces associated to generalized Hardy operators

Analysis of PDEs 2023-03-13 v2

Authors: Konstantin Merz

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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 H\"ormander 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.

Keywords

fractional laplacian hardy potential sobolev spaces horrmander multiplier theorem littlewood-paley theory

Cite

@article{arxiv.1904.07614,
  title  = {On Scales of Sobolev spaces associated to generalized Hardy operators},
  author = {Konstantin Merz},
  journal= {arXiv preprint arXiv:1904.07614},
  year   = {2023}
}

Comments

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

On Scales of Sobolev spaces associated to generalized Hardy operators

Abstract

Keywords

Cite

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