关于Carleson算子的线性化

ON THE LINEARIZATION OF THE CARLESON OPERATOR

讨论了Carleson算子C的线性化问题,证明了下面的结论:设1≤p,q<∞,则Carleson算子C为弱(p,q)型的A>0,s.t.对任一有界的阶梯函数n:R→R,均成立‖Cnf‖L(q,∞)≤A‖f‖p,f∈S.此处,Cn为C在n处的一个线性化.并且,说明了对(p,q)型有界性成立类似的结果.此外,对bi-Carleson算子也得到了对应的结论.

The following theorem be obtained that the Carleson operator l is of the weak （p,q） type if and only if there exists constant A〉0 such that the following estimate ‖lnf‖L（q,∞）≤A‖f‖p holds for all hounded function n：R→R, which is an infinite （or finite） linear combination of characteristic functions of intervals. Here, ln is the linearization of l at n.