Riesz means and bilinear Riesz means on H-type groups. (English) Zbl 07812444
Summary: In this paper, we investigate the Riesz means \(S^{\delta}\) and the bilinear Riesz means \(S^{\alpha}\) associated to the sublaplacian on H-type groups. We obtain the \(L^p\)-boundedness of \(S^{\delta}\) by using the restriction theorem on H-type groups. Our result is different from that on Heisenberg groups. We prove that \(S^{\alpha}\) is bounded from \(L^{p_1} \times L^{p_2}\) into \(L^p\) for \(1 \leq p_1, p_2 \leq \infty\) and \(1/p = 1/p_1 + 1/p_2\) when \(\alpha\) is larger than a suitable smoothness index \(\alpha (p_1, p_2)\). Because we consider H-type groups with the center dimension larger than one, it is necessary to use some different techniques from that for Heisenberg groups.
MSC:
| 43A80 | Analysis on other specific Lie groups |
| 22E30 | Analysis on real and complex Lie groups |
| 42B15 | Multipliers for harmonic analysis in several variables |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
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