Maximal function

Maximal functions play an important role in understanding, for example, the differentiability properties of functions, singular integrals and partial differential equations.

Quotes

 * It is well known that maximal functions of various types control various modes of convergence. From the classical Hardy–Littlewood maximal function to certain spherical maximal functions in Harmonic Analysis to maximal operators in Functional Analysis, this is an idea that has been played and replayed throughout analysis.