Régularité précisée des moyennes dans les équations de transport
Remarks on singular convolution operators
Restrictions from to of weak type (1,1) multipliers
Rough Marcinkiewics integral operators.
Rough Marcinkiewicz integral operators on product spaces.
In this paper, we study the Marcinkiewicz integral operators MΩ,h on the product space Rn x Rm. We prove that MΩ,h is bounded on Lp(Rn x Rm) (1< p < ∞) provided that h is a bounded radial function and Ω is a function in certain block space Bq(0,0) (Sn−1 x Sm−1) for some q > 1. We also establish the optimality of our condition in the sense that the space Bq(0,0) (Sn−1 x Sm−1) cannot be replaced by Bq(0,r) (Sn−1 x Sm−1) for any −1 < r < 0. Our results improve some...
Rough Maximal Oscillatory Singular Integral Operators
2000 Mathematics Subject Classification: Primary 42B20; Secondary 42B15, 42B25In this paper, we establish the L^p boundedness of certain maximal oscillatory singular integral operators with rough kernels belonging to certain block spaces. Our L^p boundedness result improves previously known results.
Rough singular integrals on product spaces.