摘要
证明了如果b∈BMO(R^n),对于Fefferman C.的一个经典结果(若ψ∈S(R^n)且∫ψ(x)dx= 0,那么|ψt*b(x)|2(dxdt/t)为R_+(n+1)上的Carleson测度当且仅当b∈BMO(R^n)).确定的Carleson测度,ψ的光滑性条件是不必要的.作为此结果的应用,还给出了带粗糙核的仿积的L^2有界性以及带粗糙核的Littlewood-Paley算子在BLO(R^n)上的有界性,它们分别改进了某些已知结果.
A classical result of Fefferman C. is that if ψ 6∈ S（Rn） with fψ（x）dx= 0, then {ψt＊b（x）｜2t/dxdt is a Carleson measure on R＋n＋1 if and only if b ∈ BMO（Rn）. This paper shows that if b ∈ BMO（Rn）, then the smooth condition assumed on ψ is not necessary for the Carleson measure ｜ψt＊b（x）｜2t/dxdt. As some applications of the result above, the L2 boundedness of the paraproduct πb with rough kernels and the BLO（Rn） boundedness of the Littlewood-Paley operators with rough kernel are given, which are the improvements of some known results.
出处
《数学年刊（A辑）》
CSCD
北大核心
2008年第6期801-808,共8页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10571015)
高等学校博士学科点专项科研基金(No.20050027025)资助的项目.
