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Hardy type inequalities with spherical derivatives

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Abstract

A Hardy type inequality is presented with spherical derivatives in \({\mathbb {R}}^{n}\) with \(n\ge 2\) in the framework of equalities. This clarifies the difference between contribution by radial and spherical derivatives in the improved Hardy inequality as well as nonexistence of nontrivial extremizers without compactness arguments.

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Acknowledgements

The first author was supported by JSPS KAKENHI Grant number 16H05995 and 16K1377, the second author was supported by JSPS KAKENHI Grant number JP16K05191, the third author was supported by JSPS KAKENHI Grant number 19H00644 and 18KK0073.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Saitama University, Saitama, 338-8570, Japan

    Neal Bez & Shuji Machihara

  2. Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan

    Tohru Ozawa

Authors
  1. Neal Bez
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  2. Shuji Machihara
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  3. Tohru Ozawa
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Correspondence to Shuji Machihara.

Additional information

This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.

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Bez, N., Machihara, S. & Ozawa, T. Hardy type inequalities with spherical derivatives. SN Partial Differ. Equ. Appl. 1, 5 (2020). https://doi.org/10.1007/s42985-019-0001-1

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