Wave Equation and Multiplier Estimates on Damek–ricci Spaces
نویسنده
چکیده
for arbitrary time t and arbitrary λ > 0, where ψ is a smooth bump function supported in [−2, 2] if λ < 1 and supported in [1, 2] if λ ≥ 1. This generalizes previous results in [MT]. We also prove pointwise estimates for the gradient of these convolution kernels. As a corollary, we reprove basic multiplier estimates from [HS] and [V1] and derive Sobolev estimates for the solutions to the wave equation associated to L.
منابع مشابه
The wave equation on Damek-Ricci spaces
We study the dispersive properties of the wave equation associated with the shifted Laplace–Beltrami operator on Damek–Ricci spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain global well–posedness results for the nonlinear wave equation.
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