带Hrmander型核的单边奇异积分算子的加权不等式

On Weighted Inequalities for One-Sided Singular Integrals with Hrmander Type Kernels

研究带Hrmander型核的单边奇异积分算子T^+的加权有界性.首先利用Coifman和Fefferman的好λ不等式给出T^+加权L^p(1<P<∞)有界性的一个新证明.与Lorente-Riveros-Toorre的方法相比,新方法克服了Fefferman-Stein不等式等一些经典的技术困难.利用单边C-Z分解还得到T^+的加权弱(1,1)有界性.特别地,我们证明上述加权有界性结论是最佳的.

The one-sided version of singular integral operators T＋ with HSrmander type kernels are studied. We give a new proof of the weighted Lp （1 〈 p 〈 co） bounded- ness for T＋ by adopting the well known good A inequality of Coifman and Fefferman＇s to one-sided case. As we will see in the paper, we avoid some classical techniques comparing with Lorente-Riveros-Toorre＇s theorem, such as Fefferman Stein inequal- ity. The corresponding weighted weak type （1, 1） estimates are also obtained by using one-sided C-Z decomposition. Particularly, we show that the weighted boundedness is sharp in some sense.