radial multipliers
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2018 ◽  
Vol 30 (4) ◽  
pp. 254-263 ◽  
Author(s):  
S. Lurie ◽  
D. Volkov-Bogorodskiy ◽  
E. Moiseev ◽  
A. Kholomeeva

2014 ◽  
Vol 25 (03) ◽  
pp. 1450026
Author(s):  
Sören Möller

Let ℳi be a family of II1-factors, containing a common II1-subfactor 𝒩, such that [ℳi : 𝒩] ∈ ℕ0 for all i. Furthermore, let ϕ: ℕ0 → ℂ. We show that if a Hankel matrix related to ϕ is trace-class, then there exists a unique completely bounded map Mϕ on the amalgamated free product of the ℳi with amalgamation over 𝒩, which acts as a radial multiplier. Hereby, we extend a result of Haagerup and the author for radial multipliers on reduced free products of unital C*- and von Neumann algebras.


Author(s):  
Sanghyuk Lee ◽  
Keith M. Rogers ◽  
Andreas Seeger

This chapter begins with an overview on square functions for spherical and Bochner–Riesz means which were introduced by Eli Stein, and discusses their implications for radial multipliers and associated maximal functions. It focuses on the Littlewood–Paley bounds for two square functions introduced by Stein, who had stressed their importance in harmonic analysis and many important variants and generalizations in various monographs. The chapter proves new endpoint estimates for these square functions, for the maximal Bochner–Riesz operator, and for more general classes of radial Fourier multipliers. The majority of the chapter is devoted to these proofs, such as for convolutions with spherical measures.


2012 ◽  
Vol 263 (8) ◽  
pp. 2507-2528 ◽  
Author(s):  
Uffe Haagerup ◽  
Sören Möller

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