Research interests Analysis & PDE
Area Analysis and Partial Differential Equations
Professor at UAB since 1987.
Visiting professor at University of California at Los Angeles during 1983-1984 and 2001-2002.
I contributed to the understanding of analytic capacity in a series of papers during the nineties and the beginning of 2000. I also worked on the maximal singular integral in connection with existence of principal values. More recently, I became interested in Fluid Dynamics, and I am working presently in the subject using methods from Classical Analysis.
Other Research Interests
Harmonic analysis on Euclidean spaces
- Boundary Regularity of Rotating Vortex Patches. Arch. Ration. Mech. Anal. (1) 209 (2013), 171–208. T. Hmidi, J. Mateu, J. Verdera
- Estimates for the maximal singular integral in terms of the singular integral : the case of even kernels. Ann. of Math. (3) 174 (2011), 1429–1483. J. Mateu, J. Orobitg, J. Verdera
- Extra cancellation of even Calderón-Zygmund operators and Quasiconformal mappings Authors: Journal de Mathématiques Pures et Appliqués, (4) 91 (2009), 402–431. J. Mateu, J. Orobitg, J. Verdera
- The planar Cantor sets of zero analytic capacity and the local T(b) theorem. Amer. Math. Soc. 16 (2003), 19–28. J. Mateu, X. Tolsa, J. Verdera
- The Cauchy Integral, Analytic Capacity, and Uniform Rectifiability. Annals of Mathematics, Second Series, (1) 144 (1996), 127-136. P. Mattila, M. S. Melnikov, J. Verdera