Abstract
In this article we establish pointwise estimates for a class of oscillatory integrals related to the fundamental solution of the dispersive equation ∂t u − iP (Dx)u = 0, where P(Dx) is a differential operator whose symbol P(ξ) is a real polynomial in one variable. Then we use such pointwise estimates to establish Lp–Lq estimates for the solution of this equation.
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Cui, S. Pointwise Estimates for a Class of Oscillatory Integrals and Related Lp–Lq Estimates. J Fourier Anal Appl 11, 441–457 (2005). https://doi.org/10.1007/s00041-005-4067-0
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DOI: https://doi.org/10.1007/s00041-005-4067-0