In this paper, we establish two integral inequalities for Hardy operator＇s conjugate operator at the endpoint on n-dimensional space. The operator Hn is bounded from Lxα1 （Gn） to Lxβq （Gn） with the bound explic...In this paper, we establish two integral inequalities for Hardy operator＇s conjugate operator at the endpoint on n-dimensional space. The operator Hn is bounded from Lxα1 （Gn） to Lxβq （Gn） with the bound explicitly worked out and the similar result holds for Hn＊.展开更多
In this paper we show how to construct a scaling function and an orthonor-mal wavelet basis from a multiresolution approximation using an operator theoreticmethod.
Solving partial differential equations Has not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a sy...Solving partial differential equations Has not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a system of partial differential equations.展开更多
A space Df is constructed and some characterizations of space Df are given. It is shown that the classical Fourier transform is extended to the distribution space Df, which can be embedded into the Schwartz distributi...A space Df is constructed and some characterizations of space Df are given. It is shown that the classical Fourier transform is extended to the distribution space Df, which can be embedded into the Schwartz distribution space D＇ continuously. It is also shown that D＇f is the biggest embedded subspace of D on which the extended Fourier transform, f, is a homeomorphism of D＇f onto itself.展开更多
We give some formulae for calculation of the expansions for (1) composition of step-transition operators (STO) of any two difference schemes (DS) for ODE's, (2) inverse operator of STO of any DS, and (3) conjugate...We give some formulae for calculation of the expansions for (1) composition of step-transition operators (STO) of any two difference schemes (DS) for ODE's, (2) inverse operator of STO of any DS, and (3) conjugate operator of STO of any DS.展开更多
基金Supported in part by the Natural Science Foundation of China under grant 11071250 and 11271162
文摘In this paper, we establish two integral inequalities for Hardy operator＇s conjugate operator at the endpoint on n-dimensional space. The operator Hn is bounded from Lxα1 （Gn） to Lxβq （Gn） with the bound explicitly worked out and the similar result holds for Hn＊.
基金The first author got support in part from the fund provided by the University of North Carolina at Charlotte.The second author got support from the National Natural Science Foundation of China and the Science Foundation of Zhejiang Province.
文摘In this paper we show how to construct a scaling function and an orthonor-mal wavelet basis from a multiresolution approximation using an operator theoreticmethod.
文摘Solving partial differential equations Has not only theoretical significance, but also practical value. In this paper, by the property of conjugate operator, we give a method to construct the general solutions of a system of partial differential equations.
文摘A space Df is constructed and some characterizations of space Df are given. It is shown that the classical Fourier transform is extended to the distribution space Df, which can be embedded into the Schwartz distribution space D＇ continuously. It is also shown that D＇f is the biggest embedded subspace of D on which the extended Fourier transform, f, is a homeomorphism of D＇f onto itself.
基金This research is supported by Special Funds for Major State Basic Research Projects of China (No. G1999032801-10 and No. G1999032804) by the knowledge innovation program of the Chinese Academy of Sciences and a grant (No. 19801034) from National Natura
文摘We give some formulae for calculation of the expansions for (1) composition of step-transition operators (STO) of any two difference schemes (DS) for ODE's, (2) inverse operator of STO of any DS, and (3) conjugate operator of STO of any DS.
