About Real Interpolation

Given a function, one may wonder how regular it is. Over time, various tools have been developed to characterize this. One approach is to examine the function from an uniform perspective, considering the functional spaces to which the function belongs and those it does not belong to. Some functional spaces can be defined through the interpolation of other spaces. The aim of this talk is, first and foremost, to generalize interpolation methods with the hope of creating more precise regularity spaces. An useful tool for this generalization is the use of Boyd functions, which replace the functions $t\mapsto t^\theta$ appearing in the spaces.