TWO-WEIGHT HARDY INEQUALITY ON TOPOLOGICAL MEASURE SPACES
Mynbaev K.T. Lomakina E.N.
2025L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2025#16Issue 160 - 85 pp.
We consider a Hardy type integral operator T associated with a family of open subsets Ω(t) of an open set Ω in a Hausdorff topological space X. In the inequality the measures µ, ν are σ-additive Borel measures; the weights u, v are positive and nite almost everywhere, 1 < p < ∞, 0 < q < ∞, and C > 0 is independent of f, u, v, µ, ν. We nd necessary and su cient conditions for the boundedness and compactness of the operator T and obtain two-sided estimates for its approximation numbers. All results are proved using domain partitions, thus providing a roadmap for generalizing many one-dimensional results to a Hausdorff topological space.
approximation numbers , Hardy operator , measure space , multidimensional Hardy inequality , topological space
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International School of Economics Kazakh-British Technical University, Tolebi 59, Almaty, 050000, Kazakhstan
Laboratory of Approximate Methods and Functional Analysis Computing Center Far Eastern Branch of the Russian Academy of Sciences, Kim Yu Chen 65, Khabarovsk, 680000, Russian Federation
International School of Economics Kazakh-British Technical University
Laboratory of Approximate Methods and Functional Analysis Computing Center Far Eastern Branch of the Russian Academy of Sciences
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