Endpoint estimates of positive operators in a filtered measure space

摘要

In a filtered measure space, a necessary and sufficient Sawyer type condition is given under which a positive operator is bounded from L-1 (d mu) to L-q,L-infinity(d mu) with 1 < q < infinity. This result can be recognized as the endpoint case of Tanaka and Terasawa (Arch Math (Basel) 101: 559-568, 2013, Theorem 1.1). We also establish a similar weak type inequality for generalized Doob's maximal operators.