一个从L_(ω_1)~p(0,+∞)到L_ω~p(0,+∞)的Hilbert型积分算子的有界性及范数

On the Boundedness and Norm of a Hilbert's Type Integral Operator from L_(ω_1)~p(0,+∞) to L_ω~p(0,+∞)

利用权函数方法,讨论了含参量的Hilbert型积分算子T_(λ,μ):T_(λ,μ)(f)(y)=∫_0^(+∞)(xy)~μ/|x-y|~λf(x)dx的有界性,并得到T_(λ,μ)的范数表示.

For a Hilbert＇s type integral operator with some parameters defind byT（λ,μ）：T（λ,μ）（f）（y）=∫_0^（＋∞）（xy）^μ/｜x-y｜^λf（x）dx the boundedness and norm ofT（λ,μ） are studied by using the way of weight function.