关于《REAL VARIABLE METHODS IИ HARMOИIC ANALYSIS》一书的注记

A NOTE ON《REAL-VARIABLE METHODS IN HARMONIC ANALYSIS》

本文指出了一九八六年由美国 Academic press 出版社出版的《Real—variable Methods in Harmonic Analysis》一书中三个定理的证明错误,给出了它们的正确证明方法。关于 Hardy—Littlewood 定理还给出了更一般形式的叙述和证明,对原书中定理 B 推出了更一般的结论。

This paper pointed out the proving mistakes of three theorms from the book 《Real-variable methods in harmonic analysis》 published in 1986 by Academic press,U.S.A,and concluded their correct proving methods.For the Hardy-Littlewood theorem it was given a more general ized form and proof.About the theorem B of the book it was obtained a more generalized conclusion.