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Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity

Vishvesh Kumar (UGent) , Joel Restrepo (UGent) and Michael Ruzhansky (UGent)
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Abstract
We derive asymptotic estimates for the growth of the norm of the deformed Hankel transform on the deformed Hankel-Lipschitz space defined via a generalised modulus of continuity. The established results are similar in nature to the well-known Titchmarsh theorem, which provide a characterization of the square integrable functions satisfying certain Cauchy-Lipschitz condition in terms of an asymptotic estimate for the growth of the norm of their Fourier transform. We also give some necessary conditions in terms of the generalised modulus of continuity for the boundedness of the Dunkl transform of functions in Dunkl-Lipschitz spaces, improving the Hausdorff-Young inequality for the Dunkl transform in this special scenario.
Keywords
Applied Mathematics, Mathematics (miscellaneous), Ghent Analysis & PDE center, Lipschitz type condition, modulus of continuity, Dunkl transform, generalized translation operator, asymptotic estimate, FOURIER-TRANSFORMS, SMOOTHNESS, OPERATORS

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Citation

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

MLA
Kumar, Vishvesh, et al. “Asymptotic Estimates for the Growth of Deformed Hankel Transform by Modulus of Continuity.” RESULTS IN MATHEMATICS, vol. 79, no. 1, 2024, doi:10.1007/s00025-023-02051-w.
APA
Kumar, V., Restrepo, J., & Ruzhansky, M. (2024). Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity. RESULTS IN MATHEMATICS, 79(1). https://doi.org/10.1007/s00025-023-02051-w
Chicago author-date
Kumar, Vishvesh, Joel Restrepo, and Michael Ruzhansky. 2024. “Asymptotic Estimates for the Growth of Deformed Hankel Transform by Modulus of Continuity.” RESULTS IN MATHEMATICS 79 (1). https://doi.org/10.1007/s00025-023-02051-w.
Chicago author-date (all authors)
Kumar, Vishvesh, Joel Restrepo, and Michael Ruzhansky. 2024. “Asymptotic Estimates for the Growth of Deformed Hankel Transform by Modulus of Continuity.” RESULTS IN MATHEMATICS 79 (1). doi:10.1007/s00025-023-02051-w.
Vancouver
1.
Kumar V, Restrepo J, Ruzhansky M. Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity. RESULTS IN MATHEMATICS. 2024;79(1).
IEEE
[1]
V. Kumar, J. Restrepo, and M. Ruzhansky, “Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity,” RESULTS IN MATHEMATICS, vol. 79, no. 1, 2024.
@article{01HP4NY2EAY7E7JRRY72320CBD,
  abstract     = {{We derive asymptotic estimates for the growth of the norm of the deformed Hankel transform on the deformed Hankel-Lipschitz space defined via a generalised modulus of continuity. The established results are similar in nature to the well-known Titchmarsh theorem, which provide a characterization of the square integrable functions satisfying certain Cauchy-Lipschitz condition in terms of an asymptotic estimate for the growth of the norm of their Fourier transform. We also give some necessary conditions in terms of the generalised modulus of continuity for the boundedness of the Dunkl transform of functions in Dunkl-Lipschitz spaces, improving the Hausdorff-Young inequality for the Dunkl transform in this special scenario.}},
  articleno    = {{22}},
  author       = {{Kumar, Vishvesh and Restrepo, Joel and Ruzhansky, Michael}},
  issn         = {{1422-6383}},
  journal      = {{RESULTS IN MATHEMATICS}},
  keywords     = {{Applied Mathematics,Mathematics (miscellaneous),Ghent Analysis & PDE center,Lipschitz type condition,modulus of continuity,Dunkl transform,generalized translation operator,asymptotic estimate,FOURIER-TRANSFORMS,SMOOTHNESS,OPERATORS}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{17}},
  title        = {{Asymptotic estimates for the growth of deformed Hankel transform by modulus of continuity}},
  url          = {{http://doi.org/10.1007/s00025-023-02051-w}},
  volume       = {{79}},
  year         = {{2024}},
}

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