Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature

Ruzhansky M., Yessirkegenov N.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.507, no.2, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 507 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1016/j.jmaa.2021.125795
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Keywords: Trudinger-Moser inequality, Hardy inequality, Caffarelli-Kohn-Nirenberg inequality, Riemannian manifold, Non-positive curvature, Hyperbolic space, INTERPOLATION

Abstract

In this paper we obtain Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian manifolds with non-positive sectional curvature and, in particular, a variety of new estimates on hyperbolic spaces. Moreover, in some cases we also show their equivalence with Trudinger-Moser inequalities. As consequences, the relations between the constants of these inequalities are investigated yielding asymptotically best constants in the obtained inequalities. We also obtain the corresponding uncertainty type principles. (C) 2021 The Authors. Published by Elsevier Inc.