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<p>In the foundational contributions of Ricci and Stein (Ann. Inst. Fourier (Grenoble) <b>42</b>, 637–670, <CitationRef CitationID="CR19">1992</CitationRef>) and Fefferman and Pipher (Amer. J. Math. <b>119</b>, 337–369, <CitationRef CitationID="CR5">1997</CitationRef>), the authors develeped the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p, 1&lt;p&lt;\infty ,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>p</mi> </msup> <mo>,</mo> <mn>1</mn> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mi>∞</mi> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> boundedness of multi-parameter singular integrals associated with Zygmund dilations. The objectives of this paper are twofold: first, to systematically develop the theory of Hölder spaces adapted to Zygmund dilations and establish their characterization via Littlewood-Paley theory; and second, to prove boundedness results of the multi-parameter singular integrals associated with Zygmund dilations—introduced in Han et al. (J. Geom. Anal. <b>29</b>, 2410–2455, <CitationRef CitationID="CR8">2019</CitationRef>)—on these newly defined Hölder spaces.</p>

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Boundedness of Multi-Parameter Singular Integrals on Hölder Spaces Associated with Zygmund Dilations

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Yanchang Han,
  • Yongsheng Han,
  • Yipeng Lin,
  • Chaoqiang Tan

摘要

In the foundational contributions of Ricci and Stein (Ann. Inst. Fourier (Grenoble) 42, 637–670, 1992) and Fefferman and Pipher (Amer. J. Math. 119, 337–369, 1997), the authors develeped the \(L^p, 1<p<\infty ,\) L p , 1 < p < ∞ , boundedness of multi-parameter singular integrals associated with Zygmund dilations. The objectives of this paper are twofold: first, to systematically develop the theory of Hölder spaces adapted to Zygmund dilations and establish their characterization via Littlewood-Paley theory; and second, to prove boundedness results of the multi-parameter singular integrals associated with Zygmund dilations—introduced in Han et al. (J. Geom. Anal. 29, 2410–2455, 2019)—on these newly defined Hölder spaces.