Boundedness of Marcinkiewicz integrals with mixed homogeneity along compound surfaces

Rough Marcinkiewicz Integrals On Product Spaces

In this paper, we establish an Lp boundedness result of a class of Marcinkiewicz integral operators on product domains with rough kernels.

Boundedness on Hardy-Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels

Boundedness of Marcinkiewicz Integrals with Rough Kernel on the Herz-Type Spaces

In this note, it is proved that the Marcinkiewicz integral with rough kernel defined by

Singular Integrals with Mixed Homogeneity in Product Spaces

Let Ω ∈ L(logL+)2(Sn−1 × Sm−1) (n, m 2) satisfy some cancellation conditions. We prove the Lp boundedness (1 < p < ∞ ) of the singular integral T f (x1,x2) = p. v. ∫ ∫ Rn×Rm Ω(y1,y ′ 2)h(ρ1(y1),ρ2(y2)) ρα 1 (y1)ρ β 2 (y2) f (x1 − y1,x2 − y2)dy1 dy2, where ρ1 , ρ2 are some metrics which are homogeneous with respect to certain non-isotropic dilations. We also study the above singular integral alo...

On Weighted Inequalities for Parametric Marcinkiewicz Integrals

We establish a weighted Lp boundedness of a parametric Marcinkiewicz integral operator ρ Ω,h if Ω is allowed to be in the block space B (0,−1/2) q (Sn−1) for some q > 1 and h satisfies a mild integrability condition. We apply this conclusion to obtain the weighted Lp boundedness for a class of the parametric Marcinkiewicz integral operators ∗,ρ Ω,h,λ and ρ Ω,h,S related to the Littlewood-Paley ...