Objective The proposal consists of an extensive research program to advance the understanding of singular integral operators of Harmonic Analysis in various situations on the borderline of the existing theory. This is to be achieved by a creative combination of techniques from Analysis and Probability. On top of the standard arsenal of modern Harmonic Analysis, the main probabilistic tools are the martingale transform inequalities of Burkholder, and random geometric constructions in the spirit of the random dyadic cubes introduced to Nonhomogeneous Analysis by Nazarov, Treil and Volberg.The problems to be addressed fall under the following subtitles, with many interconnections and overlap: (i) sharp weighted inequalities; (ii) nonhomogeneous singular integrals on metric spaces; (iii) local Tb theorems with borderline assumptions; (iv) functional calculus of rough differential operators; and (v) vector-valued singular integrals.Topic (i) is a part of Classical Analysis, where new methods have led to substantial recent progress, culminating in my solution in July 2010 of a celebrated problem on the linear dependence of the weighted operator norm on the Muckenhoupt norm of the weight. The proof should be extendible to several related questions, and the aim is to also address some outstanding open problems in the area.Topics (ii) and (v) deal with extensions of the theory of singular integrals to functions with more general domain and range spaces, allowing them to be abstract metric and Banach spaces, respectively. In case (ii), I have recently been able to relax the requirements on the space compared to the established theories, opening a new research direction here. Topics (iii) and (iv) are concerned with weakening the assumptions on singular integrals in the usual Euclidean space, to allow certain applications in the theory of Partial Differential Equations. The goal is to maintain a close contact and exchange of ideas between such abstract and concrete questions. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2011-StG_20101014 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Coordinator HELSINGIN YLIOPISTO Address Yliopistonkatu 3 00014 Helsingin yliopisto Finland See on map Region Manner-Suomi Helsinki-Uusimaa Helsinki-Uusimaa Activity type Higher or Secondary Education Establishments Principal investigator Tuomas Pentinpoika Hytönen (Dr.) Administrative Contact Satu Väisänen (Ms.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all HELSINGIN YLIOPISTO Finland EU contribution € 1 100 000,00 Address Yliopistonkatu 3 00014 Helsingin yliopisto See on map Region Manner-Suomi Helsinki-Uusimaa Helsinki-Uusimaa Activity type Higher or Secondary Education Establishments Principal investigator Tuomas Pentinpoika Hytönen (Dr.) Administrative Contact Satu Väisänen (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Other funding No data
