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A Remark on Davies’ Hardy Inequality

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Functional Analysis and Its Applications Aims and scope

Abstract

We give an “integration by parts” approach to Davies’ Hardy inequality. An improvement with a strictly larger Hardy weight is thereby obtained.

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Notes

  1. See, e.g., Lemma on p. 169 of Reed and Simon’s book [12].

  2. In terms of Hardy weights: \(\frac{n}{4\widetilde m(x)^2}>\frac{n}{4 m(x)^2}\).

  3. It also holds for unbounded intervals like \((-\infty,b)\) and \((a,\infty)\), but not for \(\mathbb{R}\).

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Acknowledgments

The author wishes to thank Dr. Georgios Psaradakis for his constructive criticism on “reproofs” of classical inequalities.

Funding

Research of the author is supported by the National NSF grant of China (no. 11801274). This paper was completed while the author was on a visit, funded by CSC Postdoctoral/Visiting Scholar Program (no. 202006865011), at LAGA of Université Sorbonne Paris Nord.

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Authors and Affiliations

  1. Université Sorbonne Paris Nord, Institut Galilée, LAGA, Villetaneuse, France

    Y. C. Huang

  2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, China

    Y. C. Huang

Authors
  1. Y. C. Huang
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Correspondence to Y. C. Huang.

Additional information

Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2023, Vol. 57, pp. 104–107 https://doi.org/10.4213/faa4042.

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Huang, Y.C. A Remark on Davies’ Hardy Inequality. Funct Anal Its Appl 57, 83–86 (2023). https://doi.org/10.1134/S0016266323010100

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  • DOI: https://doi.org/10.1134/S0016266323010100

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