Fourier spectrum of Clifford H-P spaces on R-+(n+1) for 1
Fourier spectrum of Clifford H-P spaces on R-+(n+1) for 1
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R- (n 1) 上 1 的 Clifford H-P 空间的傅里叶谱
DOI：
10.1016/j.jmaa.2019.123598
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发表时间：
2020
影响因子：
1.3
通讯作者：
Qian Tao
中科院分区：
文献类型：
--
作者：
Dang Pei;Mai Weixiong;Qian Tao
研究Clifford代数值哈代空间Hp（R+ n+ 1），1≤ p≤∞中函数的Fourier谱特征.即对Clifford代数值f∈ Lp（Rn），f是Hp（R+ n+ 1）中某个函数的非切边极限，1≤ p≤∞，当且仅当f ∈ Lp（Rn）= χ+ f ∈ Lp（Rn），其中χ+（χ_）= 1 2（1+ i_）|ξ _|），傅立叶变换和上述关系被适当地解释（对于分布意义上的某些情况）。这些结果进一步发展了Alan McIntosh的相关背景。作为我们结果的一个特例，向量值Clifford哈代空间函数与Stein和韦斯工作中的共轭调和系统是一致的.后者证明了当1≤ p<∞时向量值情形的相应奇异积分形式。在Stein-Weiss背景下，我们不仅得到了向量值空间的广义共轭调和系，而且得到了整个Clifford代数值哈代空间的广义共轭调和系.
This article studies the Fourier spectrum characterization of functions in the Clifford algebra-valued Hardy spaces H p (R+ n+ 1), 1≤ p≤∞. Namely, for f∈ L p (R n), Clifford algebra-valued, f is further the non-tangential boundary limit of some function in H p (R+ n+ 1), 1≤ p≤∞, if and only if f ˆ= χ+ f ˆ, where χ+(ξ _)= 1 2 (1+ i ξ _| ξ _|), the Fourier transformation and the above relation are suitably interpreted (for some cases in the distribution sense). These results further develop the relevant context of Alan McIntosh. As a particular case of our results, the vector-valued Clifford Hardy space functions are identical with the conjugate harmonic systems in the work of Stein and Weiss. The latter proved the corresponding singular integral version of the vector-valued cases for 1≤ p<∞. We also obtain the generalized conjugate harmonic systems for the whole Clifford algebra-valued Hardy spaces rather than only the vector-valued cases in the Stein-Weiss setting.