序列空间l和函数空间L之间具有齐次核的Hilbert型算子有界的参数条件

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.