Dimension results for mappings of jet space Carnot groups

Abstract

We propose analogues of horizontal and vertical projections for model filiform jet space Carnot groups. Every pair consisting of the jet of a smooth function on $\mathbb{R}$ and a vertical hyperplane with first coordinate fixed provides a splitting of a model filiform group, which induces mappings of the group. We prove Marstrand-type theorems for these mappings and determine the possible Hausdorff dimensions of images of sets under these mappings. Analogues of projections for general jet space Carnot groups could be defined similarly.