Analysis und Grenzwertsätze auf metrischen Räumen

• Applicant: Dr. Sönke Blunck
• Subject Area: Mathematics
• Term: from 2002 to 2007
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5389463

In the last years it has become a central field of mathematical research to extend classical applications of Fourier analysis on the Euclidean space to more general metric spaces. My recent research has dealt with the extension to metric spaces of one fundamental Fourier analytic tool, the Calderon-Zygmund theory. This allowed me the corresponding extension of some important applications of the classical Calderon-Zygmund theory in functional analysis. The aim of this project is the corresponding extension of some classical applications of Fourier analysis in other fields of mathematics: limit theorems in prohability theory, Hörmander's Fourier Multiplier Theorem in harmonic analysis and the Trotter Product Formula in mathematical physics. Moreover, I want to apply these limit theorems and our new Calderon-Zygmund theory in order to improve the known criteria for maximal regularity of evolution equations and for boundedness of Riesz transforms.

• DFG Programme: Research Fellowships
• International Connection: France