Eduardo Tablate, Instituto de Ciencias Matemáticas (ICMAT)
Solving a problem formulated by Mikael de la Salle, we shall present an extension of the Hörmander-Mikhlin theorem which applies beyond the context of Fourier multipliers, the so-called Schur multipliers. This objects form a class of linear maps on matrix algebras with profound connections in functional analysis, operator algebras, geometric group theory and harmonic analysis. Our main result provides a rather simple criterium for the boundedness of Schur multipliers on their natural Lp spaces, the Schatten-p classes. Finally, applications include an improvement of Arazy’s conjecture and matrix forms of Littlewood-Payley theory.
This talk is based on joint work with J. Conde, A. González and J. Parcet.