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A Note on Hardy Inequalities on Homogeneous Groups

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Abstract

We provide the necessary and sufficient characterizations on a pair of positive radial functions so that the two-weight Hardy inequalities hold true on homogeneous groups, one of most general subclasses of nilpotent Lie groups. We also present a simple condition on a couple of positive radial weight functions for the Lp −Hardy type inequalities to be valid.

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Acknowledgments

The authors would like to thank the anonymous reviewer for his/her helpful and constructive comments that greatly contributed to improving the final version of the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia and The Pacific Institute for the Mathematical Sciences, Vancouver, BC, V6T1Z4, Canada

    Nguyen Lam

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  1. Nguyen Lam
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Correspondence to Nguyen Lam.

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Research of this work was partially supported by the PIMS-Math Distinguished Post-doctoral Fellowship from the Pacific Institute for the Mathematical Sciences

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Lam, N. A Note on Hardy Inequalities on Homogeneous Groups. Potential Anal 51, 425–435 (2019). https://doi.org/10.1007/s11118-018-9717-3

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  • DOI: https://doi.org/10.1007/s11118-018-9717-3

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