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arXiv · 2103.05813

Sharp estimates of noncommutative Bochner-Riesz means on two-dimensional quantum tori

Xudong Lai
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Abstract

In this paper, we establish the full $L_p$ boundedness of noncommutative Bochner-Riesz means on two-dimensional quantum tori, which completely resolves an open problem raised in \cite{CXY13} in the sense of the $L_p$ convergence 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.

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Xudong Lai. 2021-03-10. Sharp estimates of noncommutative Bochner-Riesz means on two-dimensional quantum tori. https://doi.org/10.1007/s00220-021-04226-4

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