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

Michael Ruzhansky (UGent) and Nurgissa Yessirkegenov (UGent)
(2022) JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 507(2).
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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.
Keywords
Applied Mathematics, Analysis, Ghent Analysis & PDE center, Hyperbolic space, Non-positive curvature, Riemannian manifold, Caffarelli-Kohn-Nirenberg inequality, Hardy inequality, Trudinger-Moser inequality

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MLA
Ruzhansky, Michael, and Nurgissa Yessirkegenov. “Hardy, Weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg Type Inequalities on Riemannian Manifolds with Negative Curvature.” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 507, no. 2, Elsevier BV, 2022, doi:10.1016/j.jmaa.2021.125795.
APA
Ruzhansky, M., & Yessirkegenov, N. (2022). Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 507(2). https://doi.org/10.1016/j.jmaa.2021.125795
Chicago author-date
Ruzhansky, Michael, and Nurgissa Yessirkegenov. 2022. “Hardy, Weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg Type Inequalities on Riemannian Manifolds with Negative Curvature.” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 507 (2). https://doi.org/10.1016/j.jmaa.2021.125795.
Chicago author-date (all authors)
Ruzhansky, Michael, and Nurgissa Yessirkegenov. 2022. “Hardy, Weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg Type Inequalities on Riemannian Manifolds with Negative Curvature.” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 507 (2). doi:10.1016/j.jmaa.2021.125795.
Vancouver
1.
Ruzhansky M, Yessirkegenov N. Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 2022;507(2).
IEEE
[1]
M. Ruzhansky and N. Yessirkegenov, “Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature,” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 507, no. 2, 2022.
@article{01H25VP12RQ3YW2TRM1R8GF8GE,
  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.}},
  articleno    = {{125795}},
  author       = {{Ruzhansky, Michael and Yessirkegenov, Nurgissa}},
  issn         = {{0022-247X}},
  journal      = {{JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}},
  keywords     = {{Applied Mathematics,Analysis,Ghent Analysis & PDE center,Hyperbolic space,Non-positive curvature,Riemannian manifold,Caffarelli-Kohn-Nirenberg inequality,Hardy inequality,Trudinger-Moser inequality}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{21}},
  publisher    = {{Elsevier BV}},
  title        = {{Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature}},
  url          = {{http://doi.org/10.1016/j.jmaa.2021.125795}},
  volume       = {{507}},
  year         = {{2022}},
}
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