Characterization of weighted inequalities for superpositions of integral and supremal operators
Year: 2026
Type: article
Abstract: In this paper, we provide a characterization of the boundedness of positive sublinear operators that are superposition of three operators: Copson, Hardy, and Tandori (supremal) operators defined on the half-axis from a weighted Lebesgue space Lp(v) to another weighted Lebesgue space L1(w), where v and w are weight functions on the half-axis (0,∞), and 1 < p < ∞. Our characterization is entirely different from existing results in the literature. The motivation for investigating such inequalities stems from the problem of finding a minimal rearrangement invariant space that contains the cones of non-increasing rearrangement of the functions represented by generalized fractional maximal function acting on functions from weighted Lorentz function spaces. More specifically, by obtaining two-sided estimates for the best constant in the corresponding inequality, we derive a characterization of the associate space of minimal rearrangement invariant spaces containing cones of non-increasing rearrangement of generalized fractional maximal function. To achieve this goal, we are using discretization and anti-discretization methods. In particular, we extend existing discretization techniques to handle the operators formed by iterating the Copson, Hardy, and Tandori operators. We first establish a discrete characterization in Theorem 3. Then, applying anti-discretization techniques, we derive a continuous characterization in Theorem 1.
Authors: T. Ünver, A. Gogatishvili, N.A. Bokayev, A.N. Abek
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7166308845