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Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups

Aidyn Kassymov (UGent) , Michael Ruzhansky (UGent) and Durvudkhan Suragan
(2019) INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS. 30(8). p.643-655
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Abstract
In this note, we prove the Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy-Littlewood-Sobolev inequality on general homogeneous Lie groups.
Keywords
Riesz potential, Hardy-Littlewood-Sobolev inequality, Stein-Weiss inequality, fractional operator, fractional integral, homogeneous Lie group, WEIGHTED NORM INEQUALITIES, FRACTIONAL INTEGRALS, SHARP CONSTANTS

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Citation

Please use this url to cite or link to this publication:

MLA
Kassymov, Aidyn, et al. “Hardy-Littlewood-Sobolev and Stein-Weiss Inequalities on Homogeneous Lie Groups.” INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, vol. 30, no. 8, 2019, pp. 643–55, doi:10.1080/10652469.2019.1597080.
APA
Kassymov, A., Ruzhansky, M., & Suragan, D. (2019). Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 30(8), 643–655. https://doi.org/10.1080/10652469.2019.1597080
Chicago author-date
Kassymov, Aidyn, Michael Ruzhansky, and Durvudkhan Suragan. 2019. “Hardy-Littlewood-Sobolev and Stein-Weiss Inequalities on Homogeneous Lie Groups.” INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS 30 (8): 643–55. https://doi.org/10.1080/10652469.2019.1597080.
Chicago author-date (all authors)
Kassymov, Aidyn, Michael Ruzhansky, and Durvudkhan Suragan. 2019. “Hardy-Littlewood-Sobolev and Stein-Weiss Inequalities on Homogeneous Lie Groups.” INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS 30 (8): 643–655. doi:10.1080/10652469.2019.1597080.
Vancouver
1.
Kassymov A, Ruzhansky M, Suragan D. Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS. 2019;30(8):643–55.
IEEE
[1]
A. Kassymov, M. Ruzhansky, and D. Suragan, “Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups,” INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, vol. 30, no. 8, pp. 643–655, 2019.
@article{8636221,
  abstract     = {{In this note, we prove the Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy-Littlewood-Sobolev inequality on general homogeneous Lie groups.}},
  author       = {{Kassymov, Aidyn and Ruzhansky, Michael and Suragan, Durvudkhan}},
  issn         = {{1065-2469}},
  journal      = {{INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS}},
  keywords     = {{Riesz potential,Hardy-Littlewood-Sobolev inequality,Stein-Weiss inequality,fractional operator,fractional integral,homogeneous Lie group,WEIGHTED NORM INEQUALITIES,FRACTIONAL INTEGRALS,SHARP CONSTANTS}},
  language     = {{eng}},
  number       = {{8}},
  pages        = {{643--655}},
  title        = {{Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups}},
  url          = {{http://doi.org/10.1080/10652469.2019.1597080}},
  volume       = {{30}},
  year         = {{2019}},
}
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