Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups-Reference-Cited by-同舟云学术

Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups

Published:2021-10-06 Issue: Volume: Page:
ISSN:0010-0757
Container-title:Collectanea Mathematica
language:en
Short-container-title:Collect. Math.

Author:

Cardona Duván,Ruzhansky Michael

Abstract

AbstractWe investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the Hörmander-Mihlin-Marcinkiewicz condition. In our analysis, we use the difference structure of the unitary dual of a compact Lie group. Our results cover the sharp Hörmander-Mihlin theorem on Lebesgue spaces and also other historical results on the subject.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s13348-021-00330-9.pdf

Reference53 articles.

1. Alexopoulos, G.: Spectral multipliers on Lie groups of polynomial growth. Proc. Amer. Math. Soc. 120, 973–979 (1994)

2. Anker, J.P.: $$L^p$$-Fourier multipliers on Riemannian symmetric spaces of the noncompact type. Ann. Math. 132, 597–628 (1990)

3. Baernstein, A., II., Sawyer, E.T.: Embedding and multiplier theorems for $$H^p(R^n)$$. Mem. Amer. Math. Soc. 318 (1985)

4. Calderón, A.P., Torchinsky, A.: Parabolic maximal functions associated with a distribution. II. Adv. Math. 24, 101–171 (1977)

5. Cardona,D.: Besov continuity of pseudo-differential operators on compact Lie groups revisited. C. R. Math. Acad. Sci. Paris Vol. 355, Issue 5, May (2017), Pag. 533–537

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