Resumen de Generalized Stepanov type theorem with applications over metric-measure spaces

Alireza Ranjbar-Motlagh

• The main purpose of this article is to extend an Lp-type generalization of Stepanov's differentiability theorem in metric-measure space. This generalized Stepanov type theorem is applied to the Sobolev and bounded variation functions in order to show the Lp-type generalized differentiability for such functions. The proof of this generalized differentiability theorem is a combination of the proofs of Campanato and Stepanov theorems which is an extension of author's work to abstract spaces. Moreover, we give a positive answer to a question of Balogh-Rogovin-Zurcher about p-type generalized differentiability of BV functions over metric-measure spaces..