<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41980_2025_971_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">$f\in L^1({\mathbb {R}}^2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo>∈</mo> <msup> <mi>L</mi> <mn>1</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41980_2025_971_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\widehat{f}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>f</mi> <mo stretchy="true">^</mo> </mover> </math></EquationSource> </InlineEquation> be its double classical Fourier transform. We give necessary and sufficient conditions for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41980_2025_971_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\widehat{f}$</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>f</mi> <mo stretchy="true">^</mo> </mover> </math></EquationSource> </InlineEquation> to belong to generalized uniform Nikol’skii classes in terms of integral behavior of <i>f</i>. Several equivalence results are obtained.</p>

Double Fourier Transforms from Generalized Uniform Nikol’skii Classes

期刊论文
发表日期：

2025年7月24日

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Yulia Krotova,
Sergey Volosivets

摘要

Let $f\in L^1({\mathbb {R}}^2)$ $f \in L^{1} (R^{2})$ and $\widehat{f}$ $\hat{f}$ be its double classical Fourier transform. We give necessary and sufficient conditions for $\widehat{f}$ $\hat{f}$ to belong to generalized uniform Nikol’skii classes in terms of integral behavior of f. Several equivalence results are obtained.