The commutators of singular integral operators with homogeneous kernel(Ω(x))/(|x|~n)are studied, where Ω is homogeneous of degree zero,and has mean value zero on the unit sphere.It is proved that Ω ∈ L(logL)^(k+1)...The commutators of singular integral operators with homogeneous kernel(Ω(x))/(|x|~n)are studied, where Ω is homogeneous of degree zero,and has mean value zero on the unit sphere.It is proved that Ω ∈ L(logL)^(k+1)(S^(n-1))is a sufficient condition such that the κ-th order commutator is bounded on L^2(R^n).展开更多
This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations （DAEs）. Most of the previous works have been focused on linear variable-co...This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations （DAEs）. Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs.展开更多
基金supported by the NSF of China(19701039)partially supported by the NFS of China(19971010)Visiting Scholar Foundation of Key Lab.in Peking University
文摘The commutators of singular integral operators with homogeneous kernel(Ω(x))/(|x|~n)are studied, where Ω is homogeneous of degree zero,and has mean value zero on the unit sphere.It is proved that Ω ∈ L(logL)^(k+1)(S^(n-1))is a sufficient condition such that the κ-th order commutator is bounded on L^2(R^n).
文摘This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations （DAEs）. Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs.
