<p>In this paper we introduce the John-Nirenberg’s type spaces <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1733_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$JN _p$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>J</mi> <msub> <mi>N</mi> <mi>p</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> associated with the Gaussian measure <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1733_Article_IEq5.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="158" /> </InlineMediaObject> <EquationSource Format="TEX">$d\gamma (x) = \pi ^{-d/2}e^{-|x|^2}dx$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mi>γ</mi> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <msup> <mi>π</mi> <mrow> <mo>-</mo> <mi>d</mi> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msup> <mrow> <mo stretchy="false">|</mo> <mi>x</mi> <mo stretchy="false">|</mo> </mrow> <mn>2</mn> </msup> </mrow> </msup> <mi>d</mi> <mi>x</mi> </mrow> </math></EquationSource> </InlineEquation> in <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1733_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb {R}^d$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> where <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1733_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">$1<p<\infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo><</mo> <mi>p</mi> <mo><</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>. We prove a John-Nirenberg inequality for <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1733_Article_IEq8.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="TEX">$JN _p(\mathbb {R}^d,\gamma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>J</mi> <msub> <mi>N</mi> <mi>p</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> <mo>,</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We also characterize the predual of <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1733_Article_IEq8.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="TEX">$JN _p(\mathbb {R}^d,\gamma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>J</mi> <msub> <mi>N</mi> <mi>p</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> <mo>,</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> as a Hardy type space.</p>

Gaussian $JN _p$ Spaces

期刊论文
发表日期：

2025年6月17日

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Jorge J. Betancor,
Estefanía Dalmasso,
Pablo Quijano

摘要

In this paper we introduce the John-Nirenberg’s type spaces $JN _p$ $J N_{p}$ associated with the Gaussian measure $d\gamma (x) = \pi ^{-d/2}e^{-|x|^2}dx$ $d γ (x) = π^{- d / 2} e^{- {| x |}^{2}} d x$ in $\mathbb {R}^d$ $R^{d}$ where $1<p<\infty $ $1 < p < \infty$ . We prove a John-Nirenberg inequality for $JN _p(\mathbb {R}^d,\gamma )$ $J N_{p} (R^{d}, γ)$ . We also characterize the predual of $JN _p(\mathbb {R}^d,\gamma )$ $J N_{p} (R^{d}, γ)$ as a Hardy type space.

Gaussian \(JN _p\) Spaces

摘要