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<p>We define the Gauss and Poisson semigroups associated with the polyaxial operator and describe some of their properties.Next, by means of the Poisson semigroup, we introduce the Littlewood–Paley <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ g $</EquationSource> </InlineEquation>-function associated with the polyaxial operator, for which we prove the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ L_{\alpha}^{p} $</EquationSource> </InlineEquation>-boundedness for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$ p\in\mathopen{]}1,+\infty\mathclose{[} $</EquationSource> </InlineEquation>.</p>

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Littlewood–Paley \( g \)-Function Associated with the Polyaxial Operator

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • M. Haddad,
  • M. Mastouri

摘要

We define the Gauss and Poisson semigroups associated with the polyaxial operator and describe some of their properties.Next, by means of the Poisson semigroup, we introduce the Littlewood–Paley $ g $ -function associated with the polyaxial operator, for which we prove the $ L_{\alpha}^{p} $ -boundedness for $ p\in\mathopen{]}1,+\infty\mathclose{[} $ .