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Some Inequalities of Hardy Type Related to Witten–Laplace Operator on Smooth Metric Measure Spaces

Author

Listed:
  • Yanlin Li

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

  • Abimbola Abolarinwa

    (Department of Mathematics, University of Lagos, Akoka, Lagos 101017, Nigeria)

  • Ali H. Alkhaldi

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • Akram Ali

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

Abstract

A complete Riemannian manifold equipped with some potential function and an invariant conformal measure is referred to as a complete smooth metric measure space. This paper generalizes some integral inequalities of the Hardy type to the setting of a complete non-compact smooth metric measure space without any geometric constraint on the potential function. The adopted approach highlights some criteria for a smooth metric measure space to admit Hardy inequalities related to Witten and Witten p -Laplace operators. The results in this paper complement in several aspect to those obtained recently in the non-compact setting.

Suggested Citation

  • Yanlin Li & Abimbola Abolarinwa & Ali H. Alkhaldi & Akram Ali, 2022. "Some Inequalities of Hardy Type Related to Witten–Laplace Operator on Smooth Metric Measure Spaces," Mathematics, MDPI, vol. 10(23), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4580-:d:992210
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    References listed on IDEAS

    as
    1. Ismail Kombe & Abdullah Yener, 2016. "Weighted Hardy and Rellich type inequalities on Riemannian manifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 289(8-9), pages 994-1004, June.
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    Cited by:

    1. Yanlin Li & Sujit Bhattacharyya & Shahroud Azami & Apurba Saha & Shyamal Kumar Hui, 2023. "Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    2. Shyamal Kumar Hui & Abimbola Abolarinwa & Meraj Ali Khan & Fatemah Mofarreh & Apurba Saha & Sujit Bhattacharyya, 2023. "Li–Yau-Type Gradient Estimate along Geometric Flow," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
    3. Yanlin Li & Erhan Güler, 2023. "A Hypersurfaces of Revolution Family in the Five-Dimensional Pseudo-Euclidean Space E 2 5," Mathematics, MDPI, vol. 11(15), pages 1-12, August.

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