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

María Jesús Carro; Bae Jun Park

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

Classical Analysis and ODEs 2026-07-02 v1

Authors: María Jesús Carro , Bae Jun Park

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 Ces\`aro 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.

Keywords

weighted estimates Herz spaces Cesàro spaces multilinear operators rough singular integrals

Cite

@article{arxiv.2607.02084,
  title  = {Weighted Extensions of Stein's Theorem for Linear and Multilinear Operators},
  author = {María Jesús Carro and Bae Jun Park},
  journal= {arXiv preprint arXiv:2607.02084},
  year   = {2026}
}