What question did this study set out to answer?

To establish weighted mixed weak-type endpoint estimates for Littlewood–Paley square functions related to Schrödinger operators.

July 30, 2026AxiomsOpen Access

Weighted Mixed Weak-Type Inequalities for Littlewood–Paley Square Functions Related to Schrödinger Operators

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Randomized trial establishes weighted mixed weak-type endpoint estimates in weighted spaces, indicating potential applications in analysis.

To establish weighted mixed weak-type endpoint estimates for Littlewood–Paley square functions related to Schrödinger operators.
Used the Calderón–Zygmund decomposition adapted to the Schrödinger setting.
Analyzed the interplay between the heat semigroup and weighted spaces.
Provided estimates without invoking the associated maximal operator.
Estimates refine endpoint behavior of operators in weighted spaces, extending classical weak (1,1) bounds.
Findings are new even in unweighted settings, indicating broader applicability.
Weighted formulations lay a foundation for future developments in Fourier analysis and elliptic equations.

Zhang et al. (2026) studied this question.

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Randomized trial establishes weighted mixed weak-type endpoint estimates in weighted spaces, indicating potential applications in analysis.