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Generalised Hardy type and Rellich type inequalities on the Heisenberg group

Abimbola Abolarinwa and Michael Ruzhansky (UGent)
(2024) JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS. 15(1).
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Abstract
This paper is primarily devoted to a class of interpolation inequalities of Hardy and Rellich types on the Heisenberg group H-n. Consequently, several weighted Hardy type, Heisenberg-Pauli-Weyl uncertainty principle and Hardy-Rellich type inqualities are established on H-n. Moreover, new weighted Sobolev type embeddings are derived. Finally, an integral inequality for vector fields in a domain of the Heisenberg group is obtained, leading to several specific weighted Hardy type inequalities by making careful choices of vector fields.
Keywords
Hardy inequality, Rellich inequality, Uncertainty principle, Heisenberg group, Horizontal Laplacian, UNCERTAINTY PRINCIPLE INEQUALITIES, NIRENBERG TYPE INEQUALITIES, INTERPOLATION INEQUALITIES

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Citation

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MLA
Abolarinwa, Abimbola, and Michael Ruzhansky. “Generalised Hardy Type and Rellich Type Inequalities on the Heisenberg Group.” JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, vol. 15, no. 1, 2024, doi:10.1007/s11868-023-00575-x.
APA
Abolarinwa, A., & Ruzhansky, M. (2024). Generalised Hardy type and Rellich type inequalities on the Heisenberg group. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 15(1). https://doi.org/10.1007/s11868-023-00575-x
Chicago author-date
Abolarinwa, Abimbola, and Michael Ruzhansky. 2024. “Generalised Hardy Type and Rellich Type Inequalities on the Heisenberg Group.” JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS 15 (1). https://doi.org/10.1007/s11868-023-00575-x.
Chicago author-date (all authors)
Abolarinwa, Abimbola, and Michael Ruzhansky. 2024. “Generalised Hardy Type and Rellich Type Inequalities on the Heisenberg Group.” JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS 15 (1). doi:10.1007/s11868-023-00575-x.
Vancouver
1.
Abolarinwa A, Ruzhansky M. Generalised Hardy type and Rellich type inequalities on the Heisenberg group. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS. 2024;15(1).
IEEE
[1]
A. Abolarinwa and M. Ruzhansky, “Generalised Hardy type and Rellich type inequalities on the Heisenberg group,” JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, vol. 15, no. 1, 2024.
@article{01HP4NMT2SDCJ799QVWXTPQWG6,
  abstract     = {{This paper is primarily devoted to a class of interpolation inequalities of Hardy and Rellich types on the Heisenberg group H-n. Consequently, several weighted Hardy type, Heisenberg-Pauli-Weyl uncertainty principle and Hardy-Rellich type inqualities are established on H-n. Moreover, new weighted Sobolev type embeddings are derived. Finally, an integral inequality for vector fields in a domain of the Heisenberg group is obtained, leading to several specific weighted Hardy type inequalities by making careful choices of vector fields.}},
  articleno    = {{3}},
  author       = {{Abolarinwa, Abimbola and Ruzhansky, Michael}},
  issn         = {{1662-9981}},
  journal      = {{JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS}},
  keywords     = {{Hardy inequality,Rellich inequality,Uncertainty principle,Heisenberg group,Horizontal Laplacian,UNCERTAINTY PRINCIPLE INEQUALITIES,NIRENBERG TYPE INEQUALITIES,INTERPOLATION INEQUALITIES}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{24}},
  title        = {{Generalised Hardy type and Rellich type inequalities on the Heisenberg group}},
  url          = {{http://doi.org/10.1007/s11868-023-00575-x}},
  volume       = {{15}},
  year         = {{2024}},
}
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