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

Autor:	Lai, Xudong
Rok vydání:	2021
Předmět:	Mathematics - Operator Algebras Primary 46L52 46L51 Secondary 46B15 42B25
Druh dokumentu:	Working Paper
DOI:	10.1007/s00220-021-04226-4
Popis:	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. Comment: 37 pages, 2 figures, to appear in Comm. Math. Phys
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2103.05813 Zobrazit plný text záznamu View this record from Arxiv