与非光滑核的奇异积分相关的Toeplitz算子的双权估计

Two Weighted Estimates for Toeplitz Operator Related to Singular Integrals Operator with Non-smooth Kernels

研究了与非光滑核的奇异积分算子和加权Lipschitz函数相关的的Toeplitz算子T_b的sharp极大函数的点态估计,并应用该估计证明了Toeplitz算子T_b是从L^p(ω)到L^q(ω^(1-q))上的有界算子.此外还建立了与非光滑核的奇异积分算子和加权BMO函数相关的的Toeplitz算子T_b的sharp极大函数的点态估计,证明了这类Toeplitz算子是从L^p(μ)到L^q(ν)上的有界算子.

This paper is concerned with point, wise estimates for the sharp maximal function of the Toeplitz operators T8 related to singular integral operators with non-smooth kernel and a weighted Lipschitz function. We show that Toeplitz operator Tb is bounded from Lp（w） to Lp（wl-q）. On the other hand, we also establish pointwise estimates for the sharp maximal function of the Toeplitz operator related to singular integral operators with non-smooth kernel and a weighted BMO function and show that this Toeplitz operator Tb is bounded from LP（μ） to LP （v）.