In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2（R^n） to the Lebesgue space L^2（R^n）, which ...In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2（R^n） to the Lebesgue space L^2（R^n）, which is a substantial improvement and extension of some known results.展开更多
This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid.The layer densities are approximated b...This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid.The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid.With the proposed technique,the computation cost of collocation matrix entries is reduced from O(M2N4)to O(MN4),where N2 is the number of spherical harmonics(i.e.,size of the matrix)and M is the number of one-dimensional integration quadrature points.Numerical results demonstrate the spectral accuracy of the method.展开更多
基金NSF of China(Grant Nos.10571015 and 10826046)SRFDP of China(Grant No.20050027025)
文摘In this paper the author proves that the commutator of the Marcinkiewicz integral operator with rough variable kernel is bounded from the homogeneous Sobolev space Lγ^2（R^n） to the Lebesgue space L^2（R^n）, which is a substantial improvement and extension of some known results.
基金Financial support for this work was provided by the National Institutes of Health(grant number:1R01GM083600-01)Z.Xu is also partially supported by the Charlotte Research Institute through a Duke Postdoctoral Fellowship.
文摘This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid.The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid.With the proposed technique,the computation cost of collocation matrix entries is reduced from O(M2N4)to O(MN4),where N2 is the number of spherical harmonics(i.e.,size of the matrix)and M is the number of one-dimensional integration quadrature points.Numerical results demonstrate the spectral accuracy of the method.
