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pseudo-differential operators of Homogeneous Symbol Class Associated with the Weinstein Transform

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1533-1562页

作者： Santosh Kumar UPADHYAY Mohd SARTAJ Department of Mathematical Sciences Indian Institute of Technology(BHU)VaranasiIndia

In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are *** boundedness of pseudo-differential operators and commutator between two pseudo-differential o... 详细信息

关键词： pseudo-differential operators Homogeneous Symbol Class Weinstein Operator Sobolev space Weinstein transform

On the Sobolev Boundedness Results of the Product of pseudo-differential operators Involving a Couple of Fractional Hankel Transforms

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Acta Mathematica Sinica,English Series 2018年第2期34卷 221-232页

作者： Akhilesh PRASAD Kanailal MAHATO Department of Applied Mathematics Indian Institute of Technology (Indian School of Mines) Dhanbad-826004 India Department of Mathematics Institute of Science Banaras Hindu University Varanasi-221005 India

This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed.

关键词： pseudo-differential operators Bessel operator fractional Hankel convolution fractional Hankel integral transform Sobolev type space

Product and Commutators of pseudo-differential operators Involving Fourier–Jacobi Transform

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Communications in Mathematics and Statistics 2022年第1期10卷 67-84页

作者： Akhilesh Prasad Manoj Kumar Singh Department of Applied Mathematics Indian Institute of Technology(Indian School of Mines)Dhanbad 826004India Department of Mathematics St.Xavier’s CollegeRanchi UniversityRanchi 834001India

The purpose of this paper is to define a new symbol classand discuss the theory of two different pseudo-differential operators(p.d.o.)involving Fourier–Jacobi transform associated with a single symbol in.We also derive boundedness results for p.d.o.’s in Sobolev type ***-differential operator is developed using the product of ***,norm inequality for commutators between two pseudo-differential operators is obtained.

关键词： Jacobi functions Fourier-Jacobi transform Sobolev space pseudo-differential operators

General Formulae for Two pseudo-differential Operator

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Communications in Theoretical Physics 2008年第6期49卷 1393-1396页

作者： ZHANG Da-Jun WU Hua DENG Shu-Fang BI Jin-Bo Department of Mathematics Shanghai University Shanghai 200444 China Department of Mathematics East China University of Science and Technology Shanghai 200237 China Department of Mathematics Hangzhou Dianzi University Hangzhou 310018 China

Some general formulas in the Sato theory related to the nonisospectral KP and mKP hierarchies are derived for simplifying calculations.

关键词： Sato theory pseudo-differential operators general formulas nonisospectral KP and mKP hierar-chies

THE　UNIQUENESS　AND　CONTINUOUS　DEPENDENCE　FOR　CHARACTERISTIC　CAUCHY　PROBLEM　OF　PARTIAL　differential　EQUATIONS

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Acta Mathematica Scientia 1995年第4期15卷 442-457页

作者：栾文贵刘伟霞 Computing Center Academia Sinica Beijing China Beijing Information Technology Institute Beijing 100101 China

in this paper, we investigate the connection between the uniqueness and the continuous dependence for the Cauchy problem of linear partial differential equations with everywhere characteristic initial hypersurface. The local Carleman's estimate used by S. Alinhac and M. S. Baouendi to prove the uniqueness for the characteristic Cauchy problem is improved to the global estimate with a specific peaking weight factor. Using this estimate, we can prove similarly the uniqueness of the characteristic Cauchy problem. In particular, we derive also the continuous dependence for the solution of this problem in the function class that a certain norm is bounded by the aid of the same inference of proving the global estimate.

关键词： pseudo-differential operators Factorization Estimation.

A Note on Besov-Morrey Spaces and Triebel-Lizorkin-Morrey Spaces

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Acta Mathematica Sinica,English Series 2009年第8期25卷 1223-1242页

作者： Yoshihiro SAWANO Department of Mathematics Gakushuin University

In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces.

关键词： function spaces pseudo-differential operators Hardy spaces

The Setting of Boundary Conditions for Boundary Value Problems of Hyperbolic-elliptic Coupled Systems

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Acta Mathematicae Applicatae Sinica 2008年第3期24卷 375-390页

作者： Shu-xing Chen Ze-jun Wang Yong-qian Zhang School of Mathematical Sciences Fudan University Shanghai 200433 China

This paper is devoted to the study of the proper setting of the boundary conditions for the boundary value problems of the hyperbolic-elliptic coupled systems of first order. The wellposedness of the corresponding boundary value problems is also established. The Lopatinski conditions for the boundary value problems of the elliptic systems is then extended to the case for hyperbolic-elliptic coupled systems. The result in this paper can be applied to the Euler system in fluid dynamics, especially to give wellposed boundary value problems describing subsonic flow.

关键词： Boundary value problems hyperbolic-elliptic coupled systems pseudo-differential operators

New Characterizations of the Dual Spaces of Hardy-amalgam Spaces

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Acta Mathematica Sinica,English Series 2022年第3期38卷 519-546页

作者： Zobo Vincent de Paul ABLE Justin FEUTO Laboratoire de Mathématiques Fondamentales UFR Mathématiques et InformatiqueUniversitéFélixHouphouët-Boigny Abidjan-Cocody22B.P.582Abidjan 22Côte d’Ivoire Laboratoire de Mathématiques Fondamentales UFR Mathématiques et InformatiqueUniversitéFélixHouphouët-Boigny Abidjan-Cocody22B.P.1194Abidjan 22Côte d’Ivoire

In this paper,carrying on with our study of the Hardy-amalgam spaces H^((q,p)) and H^((q,p))_(loc)(0 详细信息

In this paper,carrying on with our study of the Hardy-amalgam spaces H^((q,p)) and H^((q,p))_(loc)(0

关键词： Amalgam spaces Hardy-amalgam spaces duality pseudo-differential operators

L^P-REGULARITY FOR A CLASS OF pseudodifferential operators IN R^n

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Journal of Partial differential Equations 2005年第3期18卷 241-262页

作者： A. Morando Dipartimento di Matematica Universita' di Torino Via Carlo Alberto 10 10123 Torino Italy

We study here a class of pseudodifferential operators with weighted symbols of Shubin type. First, we develop the basic elements of the pseudodifferential calculus for these operators, proving in particular a result of L^P-boundedness. Then we derive regularity results in the frame of suitably defined functional spaces of Sobolev type.

关键词： pseudo-differential operators Lp boundedness global hypoellipticity.