Markov-type inequalities and duality in weighted Sobolev spaces

TL;DR

This paper establishes Markov-type inequalities within weighted Sobolev spaces for generalized classical weights and explores foundational aspects of Sobolev spaces related to vector measures.

Contribution

It introduces Markov-type inequalities in weighted Sobolev spaces with generalized weights and discusses fundamental properties of Sobolev spaces associated with vector measures.

Findings

Markov-type inequalities derived for weighted Sobolev spaces

Basic properties of Sobolev spaces with vector measures established

Extension of classical inequalities to more general weighted settings

Abstract

The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as results of independent interest, some basic facts about Sobolev spaces with respect to certain vector measures are stated.