Maria Carmen Reguera awarded EPSRC first grant
Dr. Maria Carmen Reguera was awarded an EPSRC first grant in the area of Harmonic Analysis, entitled "Harmonic Analysis in rough environments". One of the fundamental questions in Harmonic Analysis concerns the study of boundedness of singular integrals in various contexts. Classically, the question of boundedness has been considered and extensively studied in particularly smooth environments. The current project is concerned with the development of a theory for singular integrals in rougher environments, namely in Lebesgue spaces where the underlying measure can be quite irregular. This theory is fundamentally motivated by questions such as the David--Semmes Conjecture in Geometric Measure Theory, the characterization of removable singularities for bounded Lipschitz harmonic functions in Complex Analysis, the study of properties of model spaces in Operator Theory and the geometric properties of harmonic measure in any domain in PDE.