AHF

The aim of this research group is to advance in the study of different harmonic, functional and complex analysis problems. Regarding harmonic analysis, the topics of interest are mainly the study of problems related to the Fourier transform restriction phenomenon to null measurement sets. This includes, for example, space-time estimates for solutions to the wave equation and the Schrödinger equation or estimates for maximal functions associated with manifolds. Likewise, the analysis of both linear and bilinear Fourier multipliers acting on different function spaces and different groups is included. Problems related to the control of oscillatory operators by positive operators in the context of sparse domination or weighted inequalities will also be studied. In relation to functional and complex analysis problems, we aim to analyse the binding of defined operators on spaces of analytic functions both with scalar and vector values, such as the composition operator or the Cesaro operator, among others. Likewise, the study of approximation in function spaces through greedy bases is also included.