变量核奇异积分和分数次微分加权范不等式

Weighted Norm Inequalities of Variable Singular Integrals and Fractional Differentiation

用T和Dγ(0≤γ≤1)分别表示变量核奇异积分和分数次微分算子.T*和T#分别为T的共轭算子及拟共轭算子.利用球调和多项式展式,本文得到了TDγ-DγT和(T*-T#)Dγ在Bωq,λ(Rn)上的有界性.同时也得到了变量核奇异积分的积T1T2和拟积T1■T2的加权范不等式.

Let T be the singular integral operator with variable kernel and Dγ(0≤γ≤1) be the fractional differentiation operator.Denote T* and T# be the adjoint of T and the pseudo-adjoint of T respectively.In this paper,via the expansion of the spherical harmonical polynomials,the boundedness on Bωq,λ(Rn) is shown to hold for TDγ-DγT and(T*-T#)Dγ.Meanwhile,the authors also establish various weighted norm inequalities for the product T1T2 and the pseudo-product T1■T2.