广义分数次积分算子交换子在Hardy空间上的有界性

Boundedness of the commutators of generalized fractional integral operators on Hardy spaces.

[b,Tl]表示由函数b∈Lipβ(Rn)与广义分数次积分算子Tl生成的交换子.在Hardy空间原子分解理论的基础上,研究了[b,Tl]在经典Hardy空间上的有界性质,证明了[b,Tl]为(Hp,Lq)有界,并且在端点情形证明了该交换子是从Hardy空间到弱Lebesgue空间有界的.

[b,T_l] is the commutator generated by generalized fractional integral operator T_l and Lipschitz function b. Using the theories of atomic decomposition of Hardy spaces, the bounded properties of these commutators on Hardy spaces have been studied. It has been proved that [b,T_l] is (H^p, L^q) bounded and is bounded from Hardy spaces into the weak Lebesgue spaces on the endpoints.