Harmonic Operators and Spectral Families in Banach Spaces,   Pedro J. Miana,   Universidad de Zaragoza, España,  Thu, 6 August, 2009,   2:00 p.m. A-233


The main aim of this talk is to extend definitions of Hilbert transform, Dirichlet and Fejér operators (defined by convolution with suitable kernels in Lebesgue spaces) in an abstract setting. We present a self-contained theory which include different approaches from other authors whose starting points were usually C0-groups or cosine functions. We characterize the geometric property of UMD spaces in terms of the Dirichlet and Fejér operators. To end, we give several particular examples and counterexamples to illustrate our results. This is a joint work with Dr. Eva Fasangov'a.