1. CMB 2010 (vol 54 pp. 126)
|Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups|
We prove that the fundamental solutions of Kohn sub-Laplacians $\Delta + i\alpha \partial_t$ on the anisotropic Heisenberg groups are tempered distributions and have meromorphic continuation in $\alpha$ with simple poles. We compute the residues and find the partial fundamental solutions at the poles. We also find formulas for the fundamental solutions for some matrix-valued Kohn type sub-Laplacians on H-type groups.
Categories:22E30, 35R03, 43A80
2. CMB 1997 (vol 40 pp. 296)
|A general approach to Littlewood-Paley theorems for orthogonal families |
A general lacunary Littlewood-Paley type theorem is proved, which applies in a variety of settings including Jacobi polynomials in $[0, 1]$, $\su$, and the usual classical trigonometric series in $[0, 2 \pi)$. The theorem is used to derive new results for $\LP$ multipliers on $\su$ and Jacobi $\LP$ multipliers.
Categories:42B25, 42C10, 43A80