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<p>This paper explores the boundedness of Fourier multipliers from <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_78_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_78_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_q\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation>. We present new results that improve upon classical theorems due to Hörmander, Lizorkin, and Marcinkiewicz. In addition, we provide necessary conditions for the boundedness of Fourier multipliers. We introduce the concept of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_78_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(M\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>M</mi> </math></EquationSource> </InlineEquation>-generalized monotone functions and sequences and derive criteria for the boundedness of Fourier multipliers corresponding to them.</p>

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\(L_p\rightarrow L_q\) boundedness of Fourier multipliers

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  • 发表日期：

    2025年6月4日

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  • M. Nursultanov

摘要

This paper explores the boundedness of Fourier multipliers from \(L_p\) L p to \(L_q\) L q . We present new results that improve upon classical theorems due to Hörmander, Lizorkin, and Marcinkiewicz. In addition, we provide necessary conditions for the boundedness of Fourier multipliers. We introduce the concept of \(M\) M -generalized monotone functions and sequences and derive criteria for the boundedness of Fourier multipliers corresponding to them.