On Damek-Ricci spaces, radial initial data in H^β with β>a/4 give almost everywhere pointwise convergence for dispersive equations with asymptotically concave phase of degree a; the threshold is sharp up to the endpoint.
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Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces
On Damek-Ricci spaces, radial initial data in H^β with β>a/4 give almost everywhere pointwise convergence for dispersive equations with asymptotically concave phase of degree a; the threshold is sharp up to the endpoint.