Some properties and integral transforms in higher spin Clifford analysis

Chao Ding
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Abstract

Rarita-Schwinger equation plays an important role in theoretical physics. Bure\v s et al. generalized it to arbitrary spin $k/2$ in 2002 in the context of Clifford algebras. In this article, we introduce the mean value property, Cauchy's estimates, and Liouville's theorem for null solutions to Rarita-Schwinger operator in Euclidean spaces. Further, we investigate boundednesses to the Teodorescu transform and its derivatives. This gives rise to a Hodge decomposition of an $L^2$ spaces in terms of the kernel space of the Rarita-Schwinger operator and it also generalizes Bergman spaces in higher spin cases. \end{abstract}
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高自旋克利福德分析中的一些性质和积分变换
Bure\v s 等人于 2002 年在克利福德代数的背景下将其推广到任意自旋 $k/2$。在本文中,我们介绍了欧几里得空间中拉里塔-施文格算子空解的均值性质、考希估计和柳维尔定理。此外,我们还研究了 Teodorescu 变换及其导数的有界性。这就产生了以拉里塔-施文格算子的核空间为条件的 $L^2$ 空间的霍奇分解,而且它还概括了更高空间情况下的伯格曼空间。\结束语
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