变量核奇异积分和分数次微分加权范不等式

用T和D^γ（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TD^γ-D^γT和（T^*-T^#）D^γ在?^q，λ_ω（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.

Weighted Norm Inequalities of Variable Singular Integrals and Fractional Differentiation

Let T be the singular integral operator with variable kernel and D^γ (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 ?^q,λ_ω (Rⁿ) is shown to hold for TD^γ-D^γT and (T^*-T^#)D^γ. Meanwhile, the authors also establish various weighted norm inequalities for the product T₁T₂ and the pseudo-product T₁°T₂.