Аннотация
Consider a Hausdorff topological space X with Borel measure ν.Let {Ω (t)} be a totally ordered family of open subsets of an open set Ω in X parameterized by t ∈ [0, ∞).This family generates a partial order in the set of functions defined on Ω.We obtain Sawyer-type bounds for a linear functional on cones of decreasing and increasing functions in weighted spaces.These results are further applied to obtain criteria of boundedness of averaging operators in those weighted spaces.