Bilinear pseudo-differential operators on local hardy spaces

2012 ◽  
Vol 28 (2) ◽  
pp. 255-266 ◽  
Author(s):  
Jiang Wei Xiao ◽  
Yin Sheng Jiang ◽  
Wen Hua Gao
Keyword(s):  
Hardy Spaces ◽  
Differential Operators ◽  
Pseudo Differential Operators ◽  
Local Hardy Spaces

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].

scholarly journals Pseudo differential operators on local Hardy spaces on chébli-teimèche hypergroups

2000 ◽  
Vol 68 (2) ◽  
pp. 202-230
Author(s):  
Walter R. Bloom ◽  
Zengfu Xu
Keyword(s):  
Hardy Spaces ◽  
Exponential Growth ◽  
Differential Operators ◽  
Pseudo Differential Operators ◽  
Local Hardy Spaces

AbstractIn this paper we consider pseudo differential operators on local Hardy spaces hp (0 < p ≤ 1) on Chébli-Trimèche hypergroups of exponential growth.

scholarly journals The continuity of pseudo-differential operators on weighted local Hardy spaces

2010 ◽  
Vol 198 (1) ◽  
pp. 69-77 ◽  
Author(s):  
Ming-Yi Lee ◽  
Chin-Cheng Lin ◽  
Ying-Chieh Lin
Keyword(s):  
Hardy Spaces ◽  
Differential Operators ◽  
Pseudo Differential Operators ◽  
Local Hardy Spaces

Pseudo-differential operators involving Fractional Fourier cosine (sine) transform

Filomat ◽  
2017 ◽  
Vol 31 (6) ◽  
pp. 1791-1801
Author(s):  
Akhilesh Prasad ◽  
Manoj Singh
Keyword(s):  
Differential Operators ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Pseudo Differential Operators
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