One-Sided Maximal Functions

Abstract

This chapter partly deals with one-sided fractional maximal functions and their various generalizations, among them one-sided maximal functions of Hormander type. We establish L p ↑L p v (1 < p ≤ q < ∞) boundedness criteria which are very easy to verify. The proofs depend heavily on the results on the Riemann-Liouville operator which were derived in the previous chapter. Then follows a study, from the point of view of boundedness and compactness, of potentials on the line, or on a bounded interval, involving power-logarithmic kernels and their multidimensional analogues as well.