H8 Functional Calculus and Mikhilin-Type Multiplier Conditions

Autores: José Esteban Galé Gimeno , Pedro José Miana Sanz
Localización: Pre-publicaciones del Seminario Matemático " García de Galdeano ", Nº. 13, 2006
Idioma: inglés
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Resumen
- 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.