适用于含旋转的奇异积分算子的齐性空间
Homogeneous spaces adapted to singular integral operators involving rotations
摘要：
函数的Calderón-Zygmund分解被用来证明奇异积分算子的弱型（1，1）有界性。在许多示例中，分解是关于对应于某个膨胀族的球族来完成的。我们研究奇异积分运营商$T$，需要更特殊的家庭的球，提供新的空间的齐型。旋转在这些球的构造中起着决定性的作用。$T$的有界性可以通过关于这个齐型空间的Calderón-Zygmund分解来证明。证明了算子$T$作用于$\LP^p(G)$的弱型（1，1）和$\LP^p$估计，其中$G$是齐次李群.我们的结果适用于设置的基础组是海森堡群和旋转是辛自同构。它们也适用于由涉及旋转的流体力学问题引起的算子。
英文摘要：
Calderón-Zygmund decompositions of functions have been used to prove weak-type (1,1) boundedness of singular integral operators. In many examples, the decomposition is done with respect to a family of balls that corresponds to some family of dilations. We study singular integral operators $T$ that require more particular families of balls, providing new spaces of homogeneous type. Rotations play a decisive role in the construction of these balls. Boundedness of $T$ can then be shown via Calderón-Zygmund decompositions with respect to this space of homogeneous type. We prove weak-type (1,1) and $\LP^p$ estimates for operators $T$ acting on $\LP^p(G)$, where $G$ is a homogeneous Lie group. Our results apply to the setting where the underlying group is the Heisenberg group and the rotations are symplectic automorphisms. They also apply to operators that arise from some hydrodynamical problem involving rotations.
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