L^p-L^q hypergeometric spectral and Fourier multipliers associated with root systems
- Author
- Vishvesh Kumar (UGent)
- Organization
- Project
- Abstract
- In this paper, we prove Hormander's L-p-L-q multiplier theorem for the hypergeometric (or Heckman-Opdam) Fourier multipliers associated with root systems for the range 1<p <= 2 <= q<infinity. We also establish the L-p-L-q boundedness of spectral multipliers of the Heckman-Opdam Laplacian and consequently we obtain time asymptotics for the L-p-L-q norms of the hypergeometric heat kernels and the Sobolev-type embedding for the Heckman-Opdam Laplacian. The proof hinges on the Paley and Hausdorff-Young-Paley inequalities for the hypergeometric Fourier transform (also known as the Heckman-Opdam transform) associated with root systems. Moreover, we also study the aforementioned spectral multiplier results in the compact Heckman-Opdam setting.
- Keywords
- Paley inequality, Haudorff-Young-Paley inequality, Heckman-Opdam transform, Hypergeometric Fourier transform, Root systems, Spectral multipliers, L-p-L-q-estimates, LAPLACE-BELTRAMI OPERATOR, HARDY-LITTLEWOOD, PALEY INEQUALITIES, SCHWARTZ SPACE, HECKMAN, OPDAM, THEOREM
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01JX3JCK2NNWVTV12DERB61KAK
- MLA
- Kumar, Vishvesh. “L^p-L^q Hypergeometric Spectral and Fourier Multipliers Associated with Root Systems.” POTENTIAL ANALYSIS, 2025, doi:10.1007/s11118-025-10213-4.
- APA
- Kumar, V. (2025). L^p-L^q hypergeometric spectral and Fourier multipliers associated with root systems. POTENTIAL ANALYSIS. https://doi.org/10.1007/s11118-025-10213-4
- Chicago author-date
- Kumar, Vishvesh. 2025. “L^p-L^q Hypergeometric Spectral and Fourier Multipliers Associated with Root Systems.” POTENTIAL ANALYSIS. https://doi.org/10.1007/s11118-025-10213-4.
- Chicago author-date (all authors)
- Kumar, Vishvesh. 2025. “L^p-L^q Hypergeometric Spectral and Fourier Multipliers Associated with Root Systems.” POTENTIAL ANALYSIS. doi:10.1007/s11118-025-10213-4.
- Vancouver
- 1.Kumar V. L^p-L^q hypergeometric spectral and Fourier multipliers associated with root systems. POTENTIAL ANALYSIS. 2025;
- IEEE
- [1]V. Kumar, “L^p-L^q hypergeometric spectral and Fourier multipliers associated with root systems,” POTENTIAL ANALYSIS, 2025.
@article{01JX3JCK2NNWVTV12DERB61KAK,
abstract = {{In this paper, we prove Hormander's L-p-L-q multiplier theorem for the hypergeometric (or Heckman-Opdam) Fourier multipliers associated with root systems for the range 1<p <= 2 <= q<infinity. We also establish the L-p-L-q boundedness of spectral multipliers of the Heckman-Opdam Laplacian and consequently we obtain time asymptotics for the L-p-L-q norms of the hypergeometric heat kernels and the Sobolev-type embedding for the Heckman-Opdam Laplacian. The proof hinges on the Paley and Hausdorff-Young-Paley inequalities for the hypergeometric Fourier transform (also known as the Heckman-Opdam transform) associated with root systems. Moreover, we also study the aforementioned spectral multiplier results in the compact Heckman-Opdam setting.}},
author = {{Kumar, Vishvesh}},
issn = {{0926-2601}},
journal = {{POTENTIAL ANALYSIS}},
keywords = {{Paley inequality,Haudorff-Young-Paley inequality,Heckman-Opdam transform,Hypergeometric Fourier transform,Root systems,Spectral multipliers,L-p-L-q-estimates,LAPLACE-BELTRAMI OPERATOR,HARDY-LITTLEWOOD,PALEY INEQUALITIES,SCHWARTZ SPACE,HECKMAN,OPDAM,THEOREM}},
language = {{eng}},
pages = {{22}},
title = {{L^p-L^q hypergeometric spectral and Fourier multipliers associated with root systems}},
url = {{http://doi.org/10.1007/s11118-025-10213-4}},
year = {{2025}},
}
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