Resumen de H8 Functional Calculus and Mikhilin-Type Multiplier Conditions

José Esteban Galé Gimeno , Pedro José Miana Sanz

• Let T be a sectorial operator. It is known that the existence of a bounded (suitably scaled) H1 calculus for T, on every sector containing the positive half-line, is equivalent to the existence of a bounded functional calculus on the Besov algebra ¿® 1;1(R+) [4]. Such an algebra includes functions de¯ned by Mikhlin-type conditions and so the Besov calculus can be seen as a result on multipliers for T. In this paper, we use fractional derivation to analyse in detail the relationship between ¿® 1;1 and Banach algebras of Mikhlin-type. As a result, we obtain a new version of the quoted equivalence.