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Hardy’s inequality for the fractional powers of the Grushin operator

  • Rakesh BalharaEmail author
Article
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Abstract

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.

Keywords

Fractional Grushin operator fractional generalized subLaplacian Hardy’s inequality ground state representation Hecke–Bochner formula 

2010 Mathematics Subject Classification

Primary: 35A23 Secondary: 26A33 26D10 42B37 42C10 47A63 

Notes

Acknowledgements

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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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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