In this paper,we prove that the commutators of maximal hypersingular integrals with rough kernels are bounded from the Sobolev space Lpγ(Rn) to the Lebesgue space Lp(Rn),which is a substantial improvement and an exte...In this paper,we prove that the commutators of maximal hypersingular integrals with rough kernels are bounded from the Sobolev space Lpγ(Rn) to the Lebesgue space Lp(Rn),which is a substantial improvement and an extension of some known results.展开更多
On the setting of the unit ball U the author considers Toeplitz operators on Bergman space.The Bergman space Bp(U) (1≤ p < ∞) is the closed subspace of the usual Lebesgue space LP(U) consisting of holomorphic fun...On the setting of the unit ball U the author considers Toeplitz operators on Bergman space.The Bergman space Bp(U) (1≤ p < ∞) is the closed subspace of the usual Lebesgue space LP(U) consisting of holomorphic functions. For a function β ∈ L2(U), the Toeplitz operator Tβ with symbol β is defined by Tβf = (βf) for function f ∈ B2(U). Here is the Bergman projection from L2(U) onto B2(U). Two bounded linear operators S, T on the Hilbert H are said to be essentially commuting on H if the commutator ST - TS is compact on H. In this paper, a criterion of essentially Toeplitz operators with the vanishing property is obtained.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10901017 and 10931001)Program for New Century Excellent Talents in University (Grant No. NCET-11-0574)Doctoral Fund of Ministry of Education of China (Grant No. 20090003110018)
文摘In this paper,we prove that the commutators of maximal hypersingular integrals with rough kernels are bounded from the Sobolev space Lpγ(Rn) to the Lebesgue space Lp(Rn),which is a substantial improvement and an extension of some known results.
文摘On the setting of the unit ball U the author considers Toeplitz operators on Bergman space.The Bergman space Bp(U) (1≤ p < ∞) is the closed subspace of the usual Lebesgue space LP(U) consisting of holomorphic functions. For a function β ∈ L2(U), the Toeplitz operator Tβ with symbol β is defined by Tβf = (βf) for function f ∈ B2(U). Here is the Bergman projection from L2(U) onto B2(U). Two bounded linear operators S, T on the Hilbert H are said to be essentially commuting on H if the commutator ST - TS is compact on H. In this paper, a criterion of essentially Toeplitz operators with the vanishing property is obtained.
