On the local boundedness of maximal H--monotone operators

TL;DR

This paper proves that maximal H-monotone operators on the Heisenberg group are locally bounded and upper semicontinuous, providing a characterization similar to Minty's theorem in this non-commutative setting.

Contribution

It establishes local boundedness and upper semicontinuity of maximal H-monotone operators on the Heisenberg group, extending classical monotonicity results to a sub-Riemannian context.

Findings

Maximal H-monotone operators are locally bounded on the Heisenberg group.

Such operators are upper semicontinuous.

A Minty-type characterization of maximal H-monotonicity is provided.

Abstract

In this paper we prove that maximal H-monotone operators $T:H^n\rightrightarrows V_1$ whose domain is all the Heisenberg group $H^n$ are locally bounded. This implies that they are upper semicontinuous. As a consequence, maximal H-monotonicity of an operator on $H^n$ can be characterized by a suitable version of Minty's type theorem.