On l'Hospital-type rules for monotonicity.
Some conditions for existence of Lipschitz selections of multifunctions with decomposable values are given.
This paper is devoted to research on local properties of functions and multidimensional singular integrals in terms of their mean oscillation. The conditions guaranteeing existence of a derivative in the L p-sense at a given point are found. Spaces which remain invariant under singular integral operators are considered.
A characterization of the weighted Hardy inequality Fu 2 C F“v 2, F(0)=F’(0)=F(1)=F’(1)=0 is given.
Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in is given.