$S^1$-bounded Fourier multipliers on $H^1(\mathbb{R})$ and functional calculus for semigroups

Loris Arnold, Christian Le Merdy, Safoura Zadeh

Let $T:H^1(\mathbb{R})\to H^1(\mathbb{R})$ be a bounded Fourier multiplier on the analytic Hardy space $H^1(\mathbb{R})\subset L^1(\mathbb{R})$ and let $m\in L^\infty({\m…