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• W4313203754 abstract "The <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript p> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:annotation encoding=application/x-tex>L^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> boundedness theory of convolution operators is based on an initial <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L squared right-arrow upper L squared> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>L^2to L^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> estimate derived from the Fourier transform. The corresponding theory of multilinear operators lacks such a simple initial estimate in view of the unavailability of Plancherel’s identity in this setting, and up to now it has not been clear what a natural initial estimate might be. In this work we obtain initial <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L squared times midline-horizontal-ellipsis times upper L squared right-arrow upper L Superscript 2 slash m> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>×<!-- × --></mml:mo> <mml:mo>⋯<!-- ⋯ --></mml:mo> <mml:mo>×<!-- × --></mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>2</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>L^2times cdots times L^2to L^{2/m}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> estimates for three types of important multilinear operators: rough singular integrals, multipliers of Hörmander type, and multipliers whose derivatives satisfy qualitative estimates. These estimates lay the foundation for the derivation of other <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript p> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:annotation encoding=application/x-tex>L^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> estimates for such operators." @default.
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• W4313203754 date "2023-02-16" @default.
• W4313203754 modified "2023-10-17" @default.
• W4313203754 title "Initial 𝐿²×⋯×𝐿² bounds for multilinear operators" @default.
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• W4313203754 doi "https://doi.org/10.1090/tran/8877" @default.
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