具有非倍测度的参数型Marcinkiewicz积分算子及交换子的有界性

Boundedness of Parametric Marcinkiewicz Integrals and Commutators with Non-doubling Measures

证明了参数型Marcinkiewicz积分Mρ以及由参数型Marcinkiewicz积分Mρ和RBMO(μ)函数生成的交换子Mρb的有界性.在M的核函数满足较强的Hrmander条件下,不仅证明了Mρ从广义Morrey空间Lp,φ(μ)到广义Morrey空间Lp,φ(μ)有界,而且也证明了Mρb从广义Morrey空间Lp,φ(μ)到广义Morrey空间Lp,φ(μ)有界.

The authors prove the boundedness of the parameter Marcinkiewicz integral Mp and the commutator generated by Mp and RBMO （μ） function. Under the assumption that the kernel satisfies certain slightly Hormandertype condition, the authors prove that both Mp and Mb^p are bounded from the generalized Morrey spaces L^p,φ （μ） to itself.