In this paper,we investigate the L^(2) boundedness of the Fourier integral operator Tφ,a with smooth and rough symbols and phase functions which satisfy certain non-degeneracy conditions.In particular,if the symbol a...In this paper,we investigate the L^(2) boundedness of the Fourier integral operator Tφ,a with smooth and rough symbols and phase functions which satisfy certain non-degeneracy conditions.In particular,if the symbol a∈L∞Smρ,the phase functionφsatisfies some measure conditions and ∇kξφ(·,ξ)L∞≤C|ξ|−k for all k≥2,ξ≠0,and some∈>0,we obtain that Tφ,a is bounded on L^(2) if m<n2 min{ρ−1,−2}.This result is a generalization of a result of Kenig and Staubach on pseudo-differential operators and it improves a result of Dos Santos Ferreira and Staubach on Fourier integral operators.Moreover,the Fourier integral operator with rough symbols and inhomogeneous phase functions we study in this paper can be used to obtain the almost everywhere convergence of the fractional Schr odinger operator.展开更多
The concept of para-product operators over locally compact Vilenkin groups is established and the applications to the para-linearization in nonlinear problems are studied. This kind of operators plays a special role i...The concept of para-product operators over locally compact Vilenkin groups is established and the applications to the para-linearization in nonlinear problems are studied. This kind of operators plays a special role in dealing with those functions which do not have the classical derivatives.展开更多
This article deals with the boundedness properties of Calderdn-Zygmund operators on Hardy spaces Hp（Rn）. We use wavelet characterization of H^P（R^n） to show that a Calderon-Zygmund operator T with T＊1 =0 is bound...This article deals with the boundedness properties of Calderdn-Zygmund operators on Hardy spaces Hp（Rn）. We use wavelet characterization of H^P（R^n） to show that a Calderon-Zygmund operator T with T＊1 =0 is bounded on H6P（R^n）, n/n＋ε zju. edu. cn 〈 p 〈 1, where ε is the regular exponent of kernel of T. This approach can be applied to the boundedness of operators on certain Hardy spaces without atomic decomposition or molecular characterization.展开更多
We discuss the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We here study the solution of that differential Equation with an inhomogeneous term, a...We discuss the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We here study the solution of that differential Equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation.展开更多
In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation wi...In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation. We there considered derivatives of a function on , when is locally integrable on , and the integral converges. We now discard the last condition that should converge, and discuss the same problem. In Appendices, polynomial form of particular solutions are given for the differential equations studied and Hermite’s differential equation with special inhomogeneous terms.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.12071437)National key R&D program of China(Grant No.2022YFA1005703)。
文摘In this paper,we investigate the L^(2) boundedness of the Fourier integral operator Tφ,a with smooth and rough symbols and phase functions which satisfy certain non-degeneracy conditions.In particular,if the symbol a∈L∞Smρ,the phase functionφsatisfies some measure conditions and ∇kξφ(·,ξ)L∞≤C|ξ|−k for all k≥2,ξ≠0,and some∈>0,we obtain that Tφ,a is bounded on L^(2) if m<n2 min{ρ−1,−2}.This result is a generalization of a result of Kenig and Staubach on pseudo-differential operators and it improves a result of Dos Santos Ferreira and Staubach on Fourier integral operators.Moreover,the Fourier integral operator with rough symbols and inhomogeneous phase functions we study in this paper can be used to obtain the almost everywhere convergence of the fractional Schr odinger operator.
基金the National Natural Science Foundation of China
文摘The concept of para-product operators over locally compact Vilenkin groups is established and the applications to the para-linearization in nonlinear problems are studied. This kind of operators plays a special role in dealing with those functions which do not have the classical derivatives.
基金Supported by National Science Council of Taiwan under Grant #NSC 99-2115-M-008-002-MY3
文摘This article deals with the boundedness properties of Calderdn-Zygmund operators on Hardy spaces Hp（Rn）. We use wavelet characterization of H^P（R^n） to show that a Calderon-Zygmund operator T with T＊1 =0 is bounded on H6P（R^n）, n/n＋ε zju. edu. cn 〈 p 〈 1, where ε is the regular exponent of kernel of T. This approach can be applied to the boundedness of operators on certain Hardy spaces without atomic decomposition or molecular characterization.
文摘We discuss the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We here study the solution of that differential Equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation.
文摘In a preceding paper, we discussed the solution of Laplace’s differential equation by using operational calculus in the framework of distribution theory. We there studied the solution of that differential equation with an inhomogeneous term, and also a fractional differential equation of the type of Laplace’s differential equation. We there considered derivatives of a function on , when is locally integrable on , and the integral converges. We now discard the last condition that should converge, and discuss the same problem. In Appendices, polynomial form of particular solutions are given for the differential equations studied and Hermite’s differential equation with special inhomogeneous terms.
