Singular integrals with rough kernels on product spaces
Abstract
Suppose that Ω(x', y') ∈ L1(Sn-1 × Sm-1) is a homogeneous function of degree zero satisfying the mean zero property (1.1), and that h(s, t) is a bounded function on R × R. The singular integral operator Tf on the product space Rn × Rm(n ≥ 2, m ≥ 2) is defined by (formula) We prove that the operator Tf is bounded in Lp(Rn × Rm), p ∈ (1, ∞), provided that Ω is a function in certain block space Bq0,1(Sn-1 × Sm-1) for some q > 1. The result answers a question posed in [JL]. We also study singular integral operators along certain surfaces.
Department(s)
Mathematics
Document Type
Article
DOI
https://doi.org/10.14492/hokmj/1351001230
Keywords
Block spaces, Product spaces, Rough kernel, Singular integrals
Publication Date
1-1-1999
Recommended Citation
Fan, Dashan, Kanghui Guo, and Yibiao Pan. "Singular integrals with rough kernels on product spaces." Hokkaido Mathematical Journal 28, no. 3 (1999): 435-460.
Journal Title
Hokkaido Mathematical Journal
