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arXiv · 2607.02084

Weighted Extensions of Stein's Theorem for Linear and Multilinear Operators

María Jesús Carro·Bae Jun Park
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Abstract

We study weighted estimates for linear and multilinear integral operators whose kernels satisfy only size conditions. Extending a theorem of E. Stein and its refinement by Soria and Weiss, we prove weighted estimates on Herz and Cesàro type spaces, together with multilinear strong-type and weak-type analogues. As applications, we derive consequences for a range of rough singular integral operators and related variants, including linear, oscillatory, and multilinear settings.

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María Jesús Carro, Bae Jun Park. 2026-07-02. Weighted Extensions of Stein's Theorem for Linear and Multilinear Operators. https://arxiv.org/abs/2607.02084

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