A Priori Estimates for Maximally Subelliptic Quadratic Forms

We prove a priori subelliptic estimates, near a non-characteristic boundary point, for the heat operators associated to a wide class of maximally subelliptic quadratic forms. This is the third paper in a series devoted to studying general maximally subelliptic boundary value problems.

💡 Research Summary

The paper establishes a priori subelliptic estimates for heat operators associated with a broad class of maximally subelliptic quadratic forms, focusing on neighborhoods of non‑characteristic boundary points. The setting is a smooth compact manifold N with boundary, equipped with a positive smooth density Vol. A finite family of smooth vector fields (W_{1},\dots,W_{r}) satisfying Hörmander’s bracket‑generating condition of order (m) is fixed. For a chosen integer (\kappa\ge1) and smooth coefficient functions (a_{\alpha,\beta}) (multi‑indices (\alpha,\beta) with (|\alpha|,|\beta|\le\kappa)), the sesquilinear form \