Anisotropic weighted Levin–Cochran–Lee type inequalities on homogeneous Lie groups

Authors

  • Michael Ruzhansky Ghent University, Department of Mathematics: Analysis, Logic and Discrete Mathematics, and Queen Mary University of London, School of Mathematical Sciences
  • Anjali Shriwastawa Banaras Hindu University, DST-Centre for Interdisciplinary Mathematical Sciences
  • Bankteshwar Tiwari Banaras Hindu University, DST-Centre for Interdisciplinary Mathematical Sciences

DOI:

https://doi.org/10.54330/afm.176976

Keywords:

Integral Hardy inequalities, anisotropic Levin–Cochran–Lee inequalities, homogeneous Lie groups, quasi-norm, weighted exponential inequalities

Abstract

In this paper, we first prove the weighted Levin–Cochran–Lee type inequalities on homogeneous Lie groups for arbitrary weights, quasi-norms, and \(L^p\)- and \(L^q\)-norms. Then, we derive a sharp weighted inequality involving specific weights given in the form of quasi-balls in homogeneous Lie groups. Finally, we also calculate the sharp constants for the aforementioned inequalities.

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Published

2025-11-06

Issue

Vol. 50 No. 2 (2025)

Section

Articles

License

Copyright (c) 2025 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Ruzhansky, M., Shriwastawa, A., & Tiwari, B. (2025). Anisotropic weighted Levin–Cochran–Lee type inequalities on homogeneous Lie groups. Annales Fennici Mathematici, 50(2), 685–701. https://doi.org/10.54330/afm.176976