Fourier multipliers on compact groups

1982 ◽  
Vol 94 (1) ◽  
pp. 69-72 ◽  
Author(s):  
T. S. Quek ◽  
Leonard Y. H. Yap
Keyword(s):  
Fourier Multipliers ◽  
Compact Groups

scholarly journals Applications of random Fourier series over compact groups to Fourier multipliers

1972 ◽  
Vol 43 (2) ◽  
pp. 531-541 ◽  
Author(s):  
Alessandro Figà-Talamanca ◽  
John Price
Keyword(s):  
Fourier Series ◽  
Fourier Multipliers ◽  
Compact Groups ◽  
Random Fourier Series

The Fourier Multipliers of p-Fourier Spaces on Compact Groups

2014 ◽  
Vol 4 (5) ◽  
pp. 667-673
Author(s):  
E. Atto ◽  
Y. Mensah ◽  
V. Assiamoua
Keyword(s):  
Fourier Multipliers ◽  
Compact Groups

Fourier transforms of lipschitz functions and fourier multipliers on compact groups

1983 ◽  
Vol 182 (4) ◽  
pp. 537-548 ◽  
Author(s):  
Tong-Seng Quek ◽  
Leonard Y. H. Yap
Keyword(s):  
Fourier Transforms ◽  
Lipschitz Functions ◽  
Fourier Multipliers ◽  
Compact Groups

scholarly journals On the vector Fourier multipliers for compact groups

2019 ◽  
Vol 3 (1) ◽  
pp. 433-439
Author(s):  
Abudulaï Issa ◽  
◽  
Yaogan Mensah ◽  
Keyword(s):  
Fourier Multipliers ◽  
Compact Groups

scholarly journals $L^{p}-L^{q}$-Maximal regularity of the Van Wijngaarden–Eringen equation in a cylindrical domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Carlos Lizama ◽  
Marina Murillo-Arcila
Keyword(s):  
Acoustic Waves ◽  
Maximal Regularity ◽  
Bubble Radius ◽  
Fourier Multipliers ◽  
Cylindrical Domain ◽  
Lebesgue Spaces ◽  
Regularity Problem ◽  
Bubbly Liquids

Abstract We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden–Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the bubbles are of uniform radius. If the dimensionless bubble radius is greater than one, we prove that the inhomogeneous version of the Van Wijngaarden–Eringen equation, in a cylindrical domain, admits maximal regularity in Lebesgue spaces. Our methods are based on the theory of operator-valued Fourier multipliers.

Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces

2020 ◽  
Vol 32 (4) ◽  
pp. 919-936 ◽  
Author(s):  
Jiao Chen ◽  
Wei Ding ◽  
Guozhen Lu
Keyword(s):  
Hardy Spaces ◽  
Differential Operators ◽  
Integral Operators ◽  
Fourier Multipliers ◽  
Regularity Of Solutions ◽  
Local Version ◽  
Fourier Integral Operators ◽  
Pseudo Differential Operators ◽  
Local Hardy Spaces ◽  
The One

AbstractAfter the celebrated work of L. Hörmander on the one-parameter pseudo-differential operators, the applications of pseudo-differential operators have played an important role in partial differential equations, geometric analysis, harmonic analysis, theory of several complex variables and other branches of modern analysis. For instance, they are used to construct parametrices and establish the regularity of solutions to PDEs such as the {\overline{\partial}} problem. The study of Fourier multipliers, pseudo-differential operators and Fourier integral operators has stimulated further such applications. It is well known that the one-parameter pseudo-differential operators are {L^{p}({\mathbb{R}^{n}})} bounded for {1<p<\infty}, but only bounded on local Hardy spaces {h^{p}({\mathbb{R}^{n}})} introduced by Goldberg in [D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 1979, 1, 27–42] for {0<p\leq 1}. Though much work has been done on the {L^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {1<p<\infty} and Hardy {H^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {0<p\leq 1} for multi-parameter Fourier multipliers and singular integral operators, not much has been done yet for the boundedness of multi-parameter pseudo-differential operators in the range of {0<p\leq 1}. The main purpose of this paper is to establish the boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces {h^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} for {0<p\leq 1} recently introduced by Ding, Lu and Zhu in [W. Ding, G. Lu and Y. Zhu, Multi-parameter local Hardy spaces, Nonlinear Anal. 184 2019, 352–380].

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