Further generalized versions of Ilmanen lemma on insertion of C-(1,omega) or C-loc(1,omega) functions

Abstract

This is a generalization of Ilmanen's lemma (which deals with linear modulus and functions on an open subset of R n). Here we extend the mentioned result from Hilbert spaces to some superreflexive spaces, in particular to L p spaces, p ELEMENT OF [2, oo).

We also prove a "global" version of Ilmanen's lemma (where a C1,ω function is inserted between functions on an interval I SUBSET OF R).

Keywords

• Ilmanen’s lemma
• C1,ω function
• semiconvex function with general modulus