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arXiv · 1204.5654

Oscillating convolution operators on the Heisenberg group

Woocheol Choi
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Abstract

In this paper, we consider oscillating convolution operotors on the Heisenberg group $H^n_a$ with respect to the norm $ρ(x,t) = ρ_1(b x, b t)$ with $ρ_1(x,t)= (|x|^4 + t^2)^{1/4}$. We obtain $L^2$ boundedness properties using the oscillatory integral estimates for degenerate phases in the Euclidean setting. Our result contains an improvement of the Lyall's result for the cases $\frac{a^2}{b^2} \geq C_β$.

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Woocheol Choi. 2012-06-13. Oscillating convolution operators on the Heisenberg group. https://arxiv.org/abs/1204.5654

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