CPAA
Remarks on some dispersive estimates
Yonggeun Cho Tohru Ozawa Suxia Xia
In this paper we consider the initial value problem for $i\partial_t u + \omega(|\nabla|) u = 0$. Under suitable smoothness and growth conditions on $\omega$, we derive dispersive estimates which is the generalization of time decay and Strichartz estimates. We unify and also simplify dispersive estimates by utilizing the Bessel function. Another main ingredient of this paper is to revisit oscillatory integrals of [2].
keywords: dispersive estimate oscillatory integral time decay Dispersive equations Bessel functions. Strichartz estimate

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