A Note on the Kolmogorov Condition of a Weak Type Operator Author: Jau-D. Chen

Abstract：

In this article we are mainly concerned with the Kolmogorov condition which is a very nice tool to study the type of an operator. It is proved that an operator T from m(Ω1) to (Ω2), is of o-finite, is of weak type (p,s), l≦ p ≦∞, 1≦s≦∞, if and only if T satisfies the Kolmogorov condition. It is also pointed out that the hypothesis "Ω2 is of a-finite", is not redundant.

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