The objective of this research group is to advance the study of various problems in harmonic, functional, and complex analysis. Regarding harmonic analysis, the topics of interest are primarily the study of problems related to the restriction of the Fourier transform to sets of zero measure. 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 groups will be studied. Problems of control of oscillatory operators by positive operators in the context of sparse domination or weighted inequalities will also be studied. Regarding problems in functional and complex analysis, the aim is to analyze the boundedness of operators defined on analytic function spaces with both scalar and vector values, such as the composition operator or the Cesàro operator, among others. Likewise, the study of approximations in function spaces through greedy bases will be studied.

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