Atomic Decomposition Theorem for Hardy spaces on Products of Siegel Upper Half Spaces and Bi-parameter Hardy Spaces
Atomic Decomposition Theorem for Hardy spaces on Products of Siegel Upper Half Spaces and Bi-parameter Hardy Spaces
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DOI：
10.1007/s12220-023-01384-w
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发表时间：
2023-08
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影响因子：
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通讯作者：
Wei Wang;Qingyan Wu
中科院分区：
文献类型：
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作者：
Wei Wang;Qingyan Wu
Siegel上半空间的积是Siegel域，其Silov边界具有Heisenberg群的积的结构.利用与次拉普拉斯算子相联系的双参数热核的再生公式，证明了在这样的区域上的全纯哈代空间中的函数有属于双参数哈代空间的边值.借助于原子分解和双参数调和分析，我们证明了Cauchy-SzegIgn投影是到全纯哈代空间的有界算子，并且任何全纯函数都可以分解为全纯原子之和.双参数原子比单参数原子复杂，全纯原子也是如此。
Products of Siegel upper half spaces are Siegel domains whose Silov boundaries have the structure of productsof Heisenberg groups. By the reproducing formula of bi-parameter heat kernel associated to sub-Laplacians, it is established that a function in holomorphic Hardy spaceon such a domain has boundary value belonging to bi-parameter Hardy space. With the help of atomic decomposition ofand bi-parameter harmonic analysis, we show that the Cauchy–Szegő projection is a bounded operator fromto holomorphic Hardy space, and any holomorphicfunction can be decomposed as a sum of holomorphic atoms. Bi-parameter atoms onare more complicated than 1-parameter ones, and so are holomorphic atoms.