Marcinkiweicz积分在加权BMO空间上的有界性

BOUNDEDNESS OF THE MARCINKIEWICZ INTEGRAL ON THE SPACE OF FUNCTIONS OF WEIGHTED BOUNDED

主要讨论了当Ω是零次齐次函数且满足Lipα-条件时,Marcinkiewicz积分算子μΩ在空wq(δ)间BMOw上有界,而当Ω满足条件∫1δ(1+｜logδ｜)σdδ<∞时,算子μΩ在空间(BMO)w0上有界.这里w是权函数.

In this paper, we will prove the boundedness of the Marcinkiewicz integral μ_Ω on the space of Functions of weighted bounded mean Oscillation. Here Ω is homogeneous of degree zero satistying, the Lip_α-conditions or a class of L^q-Dini conditions.