摘要
给出了 Polydisk D2 =D× D上小 Hankel算子 Hφ:H 2 (T2 )→ H 20 (T2 )的范数估计 ,即‖ Hφ‖ =dis(φ,H∞ L∞ (T) +L∞ H∞ (T) ) ,再结合对偶关系得出了 H10 (T2 )的分解 ,即 f∈ H10 (T2 ) ,存在 { Fi}∞1,{ Gi}∞1∈ H 2 (T2 )使得 f = ∞1Fi Gi且该函数级数按 H 1范数收敛于f .
The author obtained the norm of little Hankel operator on Polydisk -D-2=D×D-, that is:-‖H φ‖-=dis-(φ,H-∞L-∞(T)+L-∞H-∞(T))-. Combining with the classical dual relationship, the author also obtained the decomposition of functions in -H--1 0(T-2)-, that is:-f∈H--1 0(T-2)-, there exist functional sequences -｛F i｝-∞ 1,｛G i｝-∞ 1∈H-2(T-2)-. St -f=∞1F iG i-. This series of functions converge to -f- in -H-1(T-2)- norm.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2000年第3期320-324,共5页
Journal of Sichuan University(Natural Science Edition)
关键词
HANKEL算子
正交投影算子
范数
函数空间
分解
little Hankel operator
orthogonal project operator
dual relationship
Lebesgue measure
