Calderón-Zygmund算子在Hb^p空间上的有界性  

The Boundedness of Calderón-Zygmund Operators on H_b^p Spaces

作　　者：谌稳固[1] 韩永生 苗长兴[1] 

机构地区：[1]北京应用物理与计算数学研究所,北京100088 [2]美国Auburn大学数学系AL36849-5310

出　　处：《数学学报（中文版）》2008年第3期487-492,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(10771130，10571016);北京市自然科学基金(1072006)

摘　　要：众所周知,如果Calderón-Zygmund算子T满足T~*(1)=0,则算子T在H^p,n/(n+ε)<p≤1上有界.这一经典结果的最新推广形式是:如果Calderón-Zygmund算子T满足T~*(b)=0,则算子T是从经典Hardy空间H^p到一类新的Hardy空间H_b^p有界的,其中b是一个拟增长函数.本文建立了算子Tb从新的Hardy空间H_b^p到自身或到经典Hardy空间H^p的有界性,并结合已知的结果,完备了Calderón-Zygmund算子在Hardy空间上的有界性.It is well known that Calderón-Zygmund operators T are bounded on H^p for n/n＋ε 〈 P ≤ 1 provided T^＊（1） = 0. accretive function, was recently introduced A new Hardy space Hb^p, where b is a para- and the boundedness of Calderón-Zygmund operators T from the classical Hardy space H^p to the new Hardy space Hb^p was also proven if T^＊（b） = 0. In this note, the boundedness from the new Hardy space Hb^p to either Hb^p or H^p is obtained. These results together with the results mentioned above complete the boundedness of Calderón-Zygmund operators on Hardy spaces.

关 键 词：CALDERÓN-ZYGMUND算子 Hardy空间H^p和Hb^p 拟增长函数 

分 类 号：O174.2[理学—数学]