拟微分算子交换子的端点估计

Endpoint Estimates for Commutators of Pseudo differential Operators

本文给出了象征属于Hörmander类S^(m)_(ρ,δ)(R^(n))的拟微分算子T的交换子[b,T]从H^(1)(R^(n))到弱L^(1)(R^(n))以及H^(1)_(b)(R^(n))到L^(p)(R^(n))的有界性估计,其中b∈BMO(R^(n)).

In this paper,we establish two endpoint estimates for the commutator,[b,T],of a class of pseudodifferential operators T with symbols in Hörmander class S^(m)_(ρ,δ)(R^(n)).The first one is that the commutator[b,T]is bounded from Hardy space H^(1)(R^(n))into weak L^(1)(R^(n))space.The second one is an estimate in the Hardy type spaces associated with b,where b∈BMO(R^(n)).