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<p>We establish analogs of sharp weighted weak-type bounds for <i>m</i>-sublinear operators satisfying sparse form domination, including multilinear Calderón-Zygmund singular integrals. Our results, which hold for general <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\vec {p} \in [1,\infty )^m\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>p</mi> <mo stretchy="false">→</mo> </mover> <mo>∈</mo> <msup> <mrow> <mo stretchy="false">[</mo> <mn>1</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> <mi>m</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> and feature quantitative improvements, rely on new local testing conditions and good-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation> inequalities. We address weak-type bounds in both the change of measure and multiplier settings.</p>

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Weighted Weak-Type Bounds for Multilinear Singular Integrals

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月15日

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  • Zoe Nieraeth,
  • Cody B. Stockdale,
  • Brandon Sweeting

摘要

We establish analogs of sharp weighted weak-type bounds for m-sublinear operators satisfying sparse form domination, including multilinear Calderón-Zygmund singular integrals. Our results, which hold for general \(\vec {p} \in [1,\infty )^m\) p → ∈ [ 1 , ∞ ) m and feature quantitative improvements, rely on new local testing conditions and good- \(\lambda \) λ inequalities. We address weak-type bounds in both the change of measure and multiplier settings.