A problem on rough parametric Marcinkiewicz functions

On the L Boundedness of Rough Parametric Marcinkiewicz Functions

In this paper, we study the L boundedness of a class of parametric Marcinkiewicz integral operators with rough kernels in L(log L)(Sn−1). Our result in this paper solves an open problem left by the authors of ([6]).

Rough Marcinkiewicz Integral Operators

We study the Marcinkiewicz integral operator M f(x) = ( ∫∞ −∞ | ∫ |y|≤2t f (x − (y))(Ω(y)/|y|n−1)dy|2dt/22t)1/2, where is a polynomial mapping from Rn into Rd and Ω is a homogeneous function of degree zero on Rn with mean value zero over the unit sphere Sn−1. We prove an Lp boundedness result of M for rough Ω. 2000 Mathematics Subject Classification. 42B20, 42B15, 42B25.

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.

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 ...

Rough Sets, Rough Relations and Rough Functions