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<p>For multilinear pseudo-differential operators <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T_a\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>a</mi> </msub> </math></EquationSource> </InlineEquation> with multilinear Hörmander symbols <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(S_{\rho ,\rho }^{\mathcal {M}}(n,m)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>ρ</mi> <mo>,</mo> <mi>ρ</mi> </mrow> <mi mathvariant="script">M</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\rho \in (0,1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ρ</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, we establish sparse domination for these operators, which yield sharp weighted estimates that were previously unattainable via classical sharp maximal functions estimates. Our main results extend the range of decay order <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {M}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">M</mi> </math></EquationSource> </InlineEquation> of Cao–Xue–Yabuta [<CitationRef CitationID="CR3">3</CitationRef>, J. Funct. Anal., 2020] and Park–Tomita [<CitationRef CitationID="CR18">18</CitationRef>, J. Funct. Anal., 2024].</p>

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Improving sparse bounds I: Sparse domination for multilinear pseudo-differential operators

  • 期刊论文

  • 发表日期：

    2025年11月25日

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摘要

For multilinear pseudo-differential operators \(T_a\) T a with multilinear Hörmander symbols \(S_{\rho ,\rho }^{\mathcal {M}}(n,m)\) S ρ , ρ M ( n , m ) with \(\rho \in (0,1)\) ρ ∈ ( 0 , 1 ) , we establish sparse domination for these operators, which yield sharp weighted estimates that were previously unattainable via classical sharp maximal functions estimates. Our main results extend the range of decay order \(\mathcal {M}\) M of Cao–Xue–Yabuta [3, J. Funct. Anal., 2020] and Park–Tomita [18, J. Funct. Anal., 2024].