Oscillating convolution operators on the Heisenberg group

Details Oscillating convolution operators on the Heisenberg group Oscillating convolution operators on the Heisenberg group

2012-04-25

arxiv.org/abs/1204.5654v2

Mathematics

Functional Analysis

13pages, Not yet edited fully

Scientific paper

In this paper, we consider oscillating convolution operotors on the Heisenberg group $H^n_a$ with respect to the norm $\rho(x,t) = \rho_1(b x, b t)$ with $\rho_1(x,t)= (|x|^4 + t^2)^{1/4}$. 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 $\frac{a^2}{b^2} \geq C_{\beta}$.

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