Fourier multipliers in Banach function spaces with UMD concavifications

We prove various extensions of the Coifman-Rubio de Francia-Semmes multiplier theorem to operator-valued multipliers on Banach function spaces. Our results involve a new boundedness condition on sets of operators which we call $\ell^{r}(\ell^{s})$-boundedness, which implies $\mathcal{R}$-boundedness in many cases. The proofs are based on new Littlewood-Paley-Rubio de Francia-type estimates in Banach function spaces which were recently obtained by the authors

Two types of Rubio de Francia operators on Triebel--Lizorkin and Besov spaces

We discuss generalizations of Rubio de Francia's inequality for Triebel--Lizorkin and Besov spaces, continuing the research from [5]. Two versions of Rubio de Francia's operator are discussed: it is shown that a rotation factor is needed for the boundedness of the operator in some smooth spaces while it is not essential in other spaces. We study the operators on some "end" spaces of the Triebel--Lizorkin scale and then use usual interpolation methods.Comment: 12 pages, 3 figure

The figure of Ramon Llull (Raimundus Lullus) and the significance of the recent companion volume to his Latin works in the Corpus Christianorum series

The text offered here seeks to present the recent work, Fidora, A.-Rubio, J. E. (eds.), Raimundus Lullus: An Introduction to his Life, Works and Thought, CCCM 214, Turnhout: Brepols 2008, within the dual contexts of Lullian historiography and the history of Lullism, and by locating it therein aims to assess the volume's contribution to and revision of an ongoing enterprise while providing a detailed description of the work's contents.Este artículo presenta la obra de Fidora, A.-Rubio, J. E. (eds.), Raimundus Lullus: An Introduction to his Life, Works and Thought, CCCM 214, Turnhout: Brepols 2008, en el doble contexto de la historiografía luliana y de la historia del lulismo. Con eso, se pretende determinar la contribución del volumen al discurso luliano, así como a una posible revisión del mismo, mientras que se ofrece una descripción detallada de sus contenidos

Some light on Littlewood-Paley theory

The purpose of this note is to correct an error in a paper of M. Cowling, G. Fendler and J.J.F. Fournier, and to give a counterexample to a conjecture of J.-L. Rubio de Francia.Comment: 3 pages, no figures; submitted to Math Annale