On the maximal function associated to the spherical means on the Heisenberg group
On the maximal function associated to the spherical means on the Heisenberg group
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关于海森堡群上与球均值相关的极大函数
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
S. Thangavelu
中科院分区：
文献类型：
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作者：
Sayan Bagchi;S. Hait;L. Roncal;S. Thangavelu
本文讨论了n≥2时Heisenberg群H上球面极大函数的缺版和满版。通过适当地适应M. Lacey在欧几里得情况下提出的方法，我们得到了这些极大函数的稀疏界，从而得到了新的无权估计和加权估计。特别地，我们推导出在Heisenberg群上，当1 < p <∞时，与球均值相关的空极大函数的L有界性。为了证明稀疏界，我们建立了球面均值局部（单尺度）变异体的L−L估计。
In this paper we deal with lacunary and full versions of the spherical maximal function on the Heisenberg group H, for n ≥ 2. By suitable adaptation of an approach developed by M. Lacey in the Euclidean case, we obtain sparse bounds for these maximal functions, which lead to new unweighted and weighted estimates. In particular, we deduce the L boundedness, for 1 < p < ∞, of the lacunary maximal function associated to the spherical means on the Heisenberg group. In order to prove the sparse bounds, we establish L − L estimates for local (single scale) variants of the spherical means.
海森堡径向函数上的圆极大算子
DOI：
10.2422/2036-2145.202001_006
发表时间：
2022
期刊：
Annali della Scuola normale superiore di Pisa Classe di scienze
影响因子：
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作者：
Beltran, David;Guo, Shaoming;Hickman, Jonathan;Seeger, Andreas
通讯作者：
Seeger, Andreas