Article
Communications on Pure and Applied Analysis  (2020)

Hardy inequalities for the fractional powers of the Grushin operator

Song M.; Tan J.

Keywords: Fractional Grushin operator; Fractional generalized sublaplacian; Hardy's inequality; Uncertainty principle

Abstract

We establish uncertainty principles and Hardy inequalities for the fractional Grushin operator, which are reduced to those inequalities for the fractional generalized sublaplacian. The key ingredients to obtain them are an explicit integral representation and a ground state representation for the fractional powers of generalized sublaplacian.

Más información

Título de la Revista: Communications on Pure and Applied Analysis
Volumen: 19
Número: 9
Editorial: American Institute of Mathematical Sciences
Fecha de publicación: 2020
Página final: 4726
Idioma: English
DOI:

10.3934/cpaa.2020192