The authors show that the Cauchy integral operator is bounded from Hωp(R1) to hωp(R1) (the weighted local Hardy space). To prove the results, a kind of generalized atoms is introduced and a variant of weighted "Tb theorem" is considered.
In this paper, the weak type LlogL estimate for the multilinear fractional commutator is obtained by introducing a new kind of maximal operator of the multilinear fractional order associated with the mean Luxumburg norm and using the technique of sharp function.
In this paper we study a certain directional Hilbert transform and the boundedness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels. Our results are extensions of some known theorems.
CHEN Jiecheng, DING Yong & FAN Dashan Department of Mathematics, Zhejiang University (Xixi Campus), Hangzhou 310028, China
