We study classes of mappings between finite and infinite dimensional Banach spaces that are monotone and mappings which are differences of monotone mappings (DM). We prove a Radó-Reichelderfer estimate for monotone mappings in finite dimensional spaces that remains valid for DM mappings. This provides an alternative proof of the Fréchet differentiability a.e. of DM mappings. We establish a Morrey-type estimate for the distributional derivative of monotone mappings. We prove that a locally DM mapping between finite dimensional spaces is also globally DM. We introduce and study a new class of the so-called UDM mappings between Banach spaces, which generalizes the concept of curves of finite variation.

Keywords:

monotone mapping, DM mapping, Radó-Reichelderfer property, UDM mapping, differentiability monotone mapping, DM mapping, Radó-Reichelderfer property, UDM mapping, differentiability

MSC Classifications:

26B05, 46G05 show english descriptions Continuity and differentiation questions
Derivatives [See also 46T20, 58C20, 58C25] 26B05 - Continuity and differentiation questions
46G05 - Derivatives [See also 46T20, 58C20, 58C25]

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