HARDY–STEKLOV OPERATORS ON TOPOLOGICAL MEASURE SPACES
Mynbaev K.T.
July 2024Element D.O.O.
Mathematical Inequalities and Applications
2024#27Issue 3601 - 612 pp.
We give necessary and sufficient conditions on non-negative weights u,v and measures μ,v in the inequality (∫Ω |T f(x)|qu(x)dμ(x) )1/q ≤ C (∫Ω |f(x)|pv(x)dv(x) )1/p . Here the integral operator T is a Hardy-Steklov type operator associated with a family of open subsets Ω(t) of an open set Ω in a Hausdorff topological space X; μ,v are σ -additive Borel measures, and 1 < p < ∞, 0 < q < ∞. The integration in T is over domains of type Ω(b(t))Ω(a(t)) where a,b are non-negative, increasing, continuous functions on [0,∞) that vanish at zero, tend to ∞ at ∞ and satisfy a(t) < b(t) for t ∈ (0,∞). Previously such results have been known for an operator on a subset of a Euclidean space.
boundedness , compactness , Hardy-Steklov operator , weighted inequality
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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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