摘要
By using the technique of real analysis,the parameter conditions for Hilberttype series operator and integral operator T_(1)(˜a)(x)=∑∞n=1 K(n,x)a_(n),T_(2)(f)_(n)=∫+∞0 K(n,x)f(x)dx.bounded with homogeneous kernels are discussed.The necessary and sufficient conditions for T_(1):l^(α)_(p)→L^(β)_(p)^((1−p))p(0,+∞)and T_(2):L_(q)^(β)(0,+∞)→l^(α(1−q))_(q)bounded are obtained,and their norm expressions are established under certain conditions.
作者
HONG Yong
FENG Ming-jun
洪勇;冯明军(Department of Applied Mathematics,Guangzhou Huashang College,Guangzhou 511300,China;Department of Mathematics,Guangdong University of Education,Guangzhou 510303,China)
基金
Supported by Guangdong Basic and Applied Basic Research Foundation Natural Science Foundation(Grant No.2021A1515010055)
Guangzhou Science and Technology Plan Project(Grant No.202102080177).
