A Note on L~p Boundedness for Maximal Singular Integrals on Product Domains
Meng Wang · 东北数学：英文版 · 2001
The L p boundedness for maximal singular integral operators on product domainsT *f(x,y)= sup e 1,e 20∫ |u|e 1 ∫ |v|e 2 Ω(u,v)|u| n|v| m f(x-u, y-v) d u d v = sup e 1,e 20|T e 1,e 2 f(x,y)|are discussed in this paper, where Ω(u,v)∈L q(S n-1 ×S m-1 ) and ∫ S m-1 Ω(u′,v′) d v′=0, ∫ S n-1 Ω(u′,v′) d u′=0 for every u′∈S n-1 , v′∈S m-1 .