Riesz means and bilinear Riesz means on M\'{e}tivier groups
Min Wang, Hua Zhu

TL;DR
This paper studies the boundedness properties of Riesz and bilinear Riesz means on Métivier groups, extending harmonic analysis techniques to more general non-commutative structures with high-dimensional centers.
Contribution
It establishes boundedness results for Riesz means and bilinear Riesz means on Métivier groups, generalizing previous work on Heisenberg and H-type groups.
Findings
Proves $L^{p}$-boundedness of Riesz means on Métivier groups.
Establishes $L^{p_{1}} imes L^{p_{2}} ightarrow L^{p}$ boundedness for bilinear Riesz means.
Develops new methods to handle high-dimensional centers in Métivier groups.
Abstract
In this paper, we investigate the -boundedness of the Riesz means and the boundedness of the bilinear Riesz means on M\'{e}tivier groups. M\'{e}tivier groups are generalization of Heisenberg groups and general H-type groups. Because general M\'{e}tivier groups only satisfy the non-degeneracy condition and have high-dimensional centre, we have to use different methods and techniques from those on Heisenberg groups and H-type groups.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Numerical methods in inverse problems · Nonlinear Partial Differential Equations
