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arXiv 1003.03972010-03-01math.CAmath.FA

与多维 Bessel 算子相关的调和分析算子

Harmonic Analysis Operators Associated with Multidimensional Bessel Operators

J. J. Betancor, A. J. Castro, J. Curbelo

备注：: 38 pages
发表信息：: Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), 945-974
DOI：: 10.1017/S0308210511000643

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AI总结：

本文研究了多维 Bessel 算子相关的调和分析算子，证明了热半群的极大算子和 Littlewood-Paley g-函数的弱型(1,1)性质，以及 Riesz 变换的强型(p,p)和弱型(1,1)有界性。

摘要：

本文证明，由多维 Bessel 算子定义的热半群相关的极大算子和 Littlewood-Paley g-函数是弱型(1,1)的。此外，我们证明多维 Bessel 背景下的 Riesz 变换对于所有 $1<p<\infty$ 是强型(p,p)的，且是弱型(1,1)的。

英文摘要：

In this paper we establish that the maximal operator and the Littlewood-Paley g-function associated with the heat semigroup defined by multidimensional Bessel operators are of weak type (1,1). Also, we prove that Riesz transforms in the multidimensional Bessel setting are of strong type (p,p), for every $1<p<\infty$, and of weak type (1,1).

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