For s ∈ [0, 1], b ∈ ℝ and p ∈ [1, ∞), let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10114_2025_3458_Article_IEq1.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="66" /> </InlineMediaObject> <EquationSource Format="TEX">$\dot{B}_{p,\infty}^{s,b}(\mathbb{R}^{n})$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msubsup> <mrow> <mover> <mi>B</mi> <mo>˙</mo> </mover> </mrow> <mrow> <mi>p</mi> <mo>,</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>b</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> be the logarithmic-Gagliardo–Lipschitz space, which arises as a limiting interpolation space and coincides to the classical Besov space when b = 0 and s ∈ (0, 1). In this paper, the authors study restricting principles of the Riesz potential space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10114_2025_3458_Article_IEq2.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="97" /> </InlineMediaObject> <EquationSource Format="TEX">$\cal{I}_{\alpha}(\dot{B}_{p,\infty}^{s,b}(\mathbb{R}^{n}))$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mi mathvariant="script">I</mi> </mrow> <mrow> <mi>α</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msubsup> <mrow> <mover> <mi>B</mi> <mo>˙</mo> </mover> </mrow> <mrow> <mi>p</mi> <mo>,</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>b</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> into certain Radon–Campanato space.

Restricting Riesz–Logarithmic-Gagliardo–Lipschitz Potentials

期刊论文
发表日期：

2025年1月15日

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Xinting Hu,
Liguang Liu

摘要

For s ∈ [0, 1], b ∈ ℝ and p ∈ [1, ∞), let $\dot{B}_{p,\infty}^{s,b}(\mathbb{R}^{n})$ ${\dot{B}}_{p, \infty}^{s, b} (R^{n})$ be the logarithmic-Gagliardo–Lipschitz space, which arises as a limiting interpolation space and coincides to the classical Besov space when b = 0 and s ∈ (0, 1). In this paper, the authors study restricting principles of the Riesz potential space $\cal{I}_{\alpha}(\dot{B}_{p,\infty}^{s,b}(\mathbb{R}^{n}))$ $I_{α} ({\dot{B}}_{p, \infty}^{s, b} (R^{n}))$ into certain Radon–Campanato space.