ANALYSIS ON SEMIDIRECT PRODUCTS AND HARMONIC MAPS
Glasgow mathematical journal, Tome 47 (2005) no. 2, pp. 291-302
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We study the analysis of a probability density $K$ on a Lie group $G$, where $G$ is a semidirect product of a compact group $M$ with a nilpotent group $N$. To approximate analysis on $G$ with analysis on $N$, it is natural to consider certain maps (“realizations”) of $G$ onto $N$. In this paper, we prove the existence of a realization of $G$ in $N$ which is $K$-harmonic (modulo the commutator subgroup of $N$). By utilizing this result and extending some ideas of Alexopoulos, we can prove the boundedness in $L^p$ spaces of some new Riesz transforms associated with $K$, and obtain new regularity estimates for the convolution powers of $K$.
DUNGEY, NICK. ANALYSIS ON SEMIDIRECT PRODUCTS AND HARMONIC MAPS. Glasgow mathematical journal, Tome 47 (2005) no. 2, pp. 291-302. doi: 10.1017/S0017089505002508
@article{10_1017_S0017089505002508,
author = {DUNGEY, NICK},
title = {ANALYSIS {ON} {SEMIDIRECT} {PRODUCTS} {AND} {HARMONIC} {MAPS}},
journal = {Glasgow mathematical journal},
pages = {291--302},
year = {2005},
volume = {47},
number = {2},
doi = {10.1017/S0017089505002508},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002508/}
}
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