Particular Cases at Infinity : A Never-Ending Story

Many classical function spaces are organised in families depending on a parameter, usually denoted p or q, ranging from one to infinity. For most values, these spaces behave in a regular and predictable way. However, the endpoint corresponding to infinity often stands apart.

This talk illustrates this recurring phenomenon through familiar examples such as Lebesgue spaces and duality, where the infinite case already shows unusual behaviour. The same pattern appears in real interpolation theory: while everything works smoothly for finite parameters, the case corresponding to infinity breaks a key property, namely the density of the intersection.