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 On the norm of the operator $aI+bH$ on $L^p(\mathbb R)$ Bull. Korean Math. Soc. 2018 Vol. 55, No. 4, 1209-1219 https://doi.org/10.4134/BKMS.b170676Published online July 31, 2018 Yong Ding, Loukas Grafakos, Kai Zhu Beijing Normal University, University of Missouri, Beijing Normal University Abstract : 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 Downloads: Full-text PDF