Hardy’s inequality for the fractional powers of the Grushin operator
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We prove Hardy’s inequality for the fractional powers of the generalized subLaplacian and the fractional powers of the Grushin operator. We also find an integral representation and a ground state representation for the fractional powers of the generalized subLaplacian.
KeywordsFractional Grushin operator fractional generalized subLaplacian Hardy’s inequality ground state representation Hecke–Bochner formula
2010 Mathematics Subject ClassificationPrimary: 35A23 Secondary: 26A33 26D10 42B37 42C10 47A63
The author is financially supported by UGC-CSIR. He would also like to thank his guide Prof. S Thangavelu for his continuous help and suggestions.
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