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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… Click to show full 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 Hormander 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:
associated generalized;
hardy;
spaces associated;
scales sobolev;
sobolev spaces;
generalized hardy
Journal Title: Mathematische Zeitschrift
Year Published: 2021
Link to full text (if available)
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Journal Title: Mathematische Zeitschrift
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!