Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

Let t be the singular integral operator with variable kernel defined by tf(x)=p.v.∫rn(ω(x,x-y)/x-yn)f(y)dy and let dγ (0≤γ≤1) be the fractional differentiation operator. let tand t be the adjoint of t and the pseudoadjoint of t,respectively. in this paper,the authors prove that tdγ-dγt and (t-t)dγ are bounded,respectively,from morrey-herz spaces mkp,1α,(rn) to the weak morrey-herz spaces wmkp,1α,(rn) by using the spherical harmonic decomposition. furthermore,several norm inequalities for the product t1t2 and the pseudoproduct t1°t2 are also given. © 2017 yanqi yang and shuangping tao.