Об операторе Кальдерона

Abstract

The Calderon type operator $$Sx(t) = \int\limits_0^\infty {x(s)d\mathop {\min }\limits_{i = 0,1} \{ \varphi _i (s)/\Psi _\iota (t)\} } $$ is investigated from the point of view of its bounded action in symmetric spaces of measurable functions on [0, ∞), whereφi(t) andΨi(t) are concave positive functions on [0, ∞). The following assertions are proved.