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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India

    Rakesh Balhara

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  1. Rakesh Balhara
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Correspondence to Rakesh Balhara.

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Communicating Editor: E K Narayanan

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Balhara, R. Hardy’s inequality for the fractional powers of the Grushin operator. Proc Math Sci 129, 33 (2019). https://doi.org/10.1007/s12044-019-0471-2

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  • DOI: https://doi.org/10.1007/s12044-019-0471-2

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