Inequalities for the truncated Hilbert transform and the segment multiplier

Abstract The paper is devoted to the study of LlogL inequalities and other related bounds for two classical operators on the real line: the truncated Hilbert transform and the segment multiplier. Using duality, these estimates are deduced from corresponding sharp exponential-type bounds, the proofs...
Ausführliche Beschreibung

Abstract The paper is devoted to the study of LlogL inequalities and other related bounds for two classical operators on the real line: the truncated Hilbert transform and the segment multiplier. Using duality, these estimates are deduced from corresponding sharp exponential-type bounds, the proofs of which rest on the construction of appropriate harmonic functions on the strip %$[-1,1]\times \mathbb{R }%$ and transference-type arguments. Ausführliche Beschreibung