Sharp Estimates of Noncommutative Bochner-Riesz Means on Two-Dimensional Quantum Tori
Sharp Estimates of Noncommutative Bochner-Riesz Means on Two-Dimensional Quantum Tori
复制标题
二维量子环上非交换 Bochner-Riesz 均值的锐估计
DOI：
10.1007/s00220-021-04226-4
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发表时间：
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影响因子：
2.4
通讯作者：
Xudong Lai
中科院分区：
文献类型：
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作者：
Xudong Lai
In this paper, we establish the fullboundedness of noncommutative Bochner–Riesz means on two-dimensional quantum tori, which completely resolves an open problem raised in Chen et al. (Commun Math Phys 322(3):755–805, 2013) in the sense of theconvergence for two dimensions. The main ingredients are sharp estimates of noncommutative Kakeya maximal functions and geometric estimates in the plane. We make the most of noncommutative theories of maximal/square functions, together with microlocal decompositions in both proofs of sharper estimates of Kakeya maximal functions and Bochner–Riesz means.
