Sergi Aria: Weighted Inequalities for the Hardy Operator

This talk revolves around Hardy's integral inequality, proved by G. H. Hardy in 1925. This inequality has been studied by a large number of authors during the twentieth century and has given a cause for some lines of study which are currently active. I will talk about the classical Hardy's integral inequality and its generalizations, focusing in the case of monotone functions. This point of view will make appear connections with the boundedness of the Hardy-Littlewood maximal operator and the normability of classical Lorentz spaces.