Hardy Inequalities on Cones of Monotone Functions on a Measure Space
Mynbaev K.
July 2025Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan
Azerbaijan Journal of Mathematics
2025#15Issue 265 - 84 pp.
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.
Hardy inequality , Hausdorff space , inequality on decreasing and increasing functions , Steklov operator
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International School of Economics, Kazakh-British Technical University, Tolebi 59, Almaty, 050000, Kazakhstan
International School of Economics
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