L^p‐bounds in Safarov pseudo‐differential calculus on manifolds with bounded geometry
- Author
- David Santiago Gómez Cobos (UGent) and Michael Ruzhansky (UGent)
- Organization
- Project
- Abstract
- Given a smooth complete Riemannian manifold with bounded geometry (M,g) and a linear connection del on it (not necessarily a metric one), we prove the L-p-boundedness of operators belonging to the global pseudo-differential classes Psi(m )(rho,delta)(Omega(kappa), del, tau) constructed by Safarov. Our result recovers classical Fefferman's theorem, and extends it to the following two situations: rho>1/3 and del symmetric; and del flat with any values of rho and delta. Moreover, as a consequence of our main result, we obtain boundedness on Sobolev and Besov spaces and some L-p-L-q boundedness. Different examples and applications are presented.
- Keywords
- Ghent Analysis & PDE center, OPERATORS, SPACES
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01JX2NSFHE1C2XX5Q4EJTG6N89
- MLA
- Gómez Cobos, David Santiago, and Michael Ruzhansky. “L^p‐bounds in Safarov Pseudo‐differential Calculus on Manifolds with Bounded Geometry.” JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, vol. 111, no. 4, 2025, doi:10.1112/jlms.70145.
- APA
- Gómez Cobos, D. S., & Ruzhansky, M. (2025). L^p‐bounds in Safarov pseudo‐differential calculus on manifolds with bounded geometry. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 111(4). https://doi.org/10.1112/jlms.70145
- Chicago author-date
- Gómez Cobos, David Santiago, and Michael Ruzhansky. 2025. “L^p‐bounds in Safarov Pseudo‐differential Calculus on Manifolds with Bounded Geometry.” JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES 111 (4). https://doi.org/10.1112/jlms.70145.
- Chicago author-date (all authors)
- Gómez Cobos, David Santiago, and Michael Ruzhansky. 2025. “L^p‐bounds in Safarov Pseudo‐differential Calculus on Manifolds with Bounded Geometry.” JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES 111 (4). doi:10.1112/jlms.70145.
- Vancouver
- 1.Gómez Cobos DS, Ruzhansky M. L^p‐bounds in Safarov pseudo‐differential calculus on manifolds with bounded geometry. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES. 2025;111(4).
- IEEE
- [1]D. S. Gómez Cobos and M. Ruzhansky, “L^p‐bounds in Safarov pseudo‐differential calculus on manifolds with bounded geometry,” JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, vol. 111, no. 4, 2025.
@article{01JX2NSFHE1C2XX5Q4EJTG6N89,
abstract = {{Given a smooth complete Riemannian manifold with bounded geometry (M,g) and a linear connection del on it (not necessarily a metric one), we prove the L-p-boundedness of operators belonging to the global pseudo-differential classes Psi(m )(rho,delta)(Omega(kappa), del, tau) constructed by Safarov. Our result recovers classical Fefferman's theorem, and extends it to the following two situations: rho>1/3 and del symmetric; and del flat with any values of rho and delta. Moreover, as a consequence of our main result, we obtain boundedness on Sobolev and Besov spaces and some L-p-L-q boundedness. Different examples and applications are presented.}},
articleno = {{e70145}},
author = {{Gómez Cobos, David Santiago and Ruzhansky, Michael}},
issn = {{0024-6107}},
journal = {{JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES}},
keywords = {{Ghent Analysis & PDE center,OPERATORS,SPACES}},
language = {{eng}},
number = {{4}},
pages = {{44}},
title = {{L^p‐bounds in Safarov pseudo‐differential calculus on manifolds with bounded geometry}},
url = {{http://doi.org/10.1112/jlms.70145}},
volume = {{111}},
year = {{2025}},
}
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