Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2018; 55(4): 1209-1219

Online first article July 6, 2018      Printed July 31, 2018

https://doi.org/10.4134/BKMS.b170676

Copyright © The Korean Mathematical Society.

On the norm of the operator $aI+bH$ on $L^p(\mathbb R)$

Yong Ding, Loukas Grafakos, Kai Zhu

Beijing Normal University, University of Missouri, Beijing Normal University

Abstract

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We provide a direct proof of the following theorem of Kalton, Hollenbeck, and Verbitsky \cite{HKV}: let $H$ be the Hilbert transform and let $a,b$ be real constants. Then for $12$.

Keywords: best constants, Hilbert transform

MSC numbers: Primary 42A45; Secondary 42A50, 42A99

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