Pointwise Estimates for a Class of Oscillatory Integralsand Related Lp–Lq Estimates |
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| Authors: | Shangbin Cui |
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| Affiliation: | (1) Institute of Mathematics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, People’s Republic of China |
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| Abstract: | In this article we establish pointwise estimates for a class of oscillatory integralsrelated 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 usesuch pointwise estimates to establish Lp–Lq estimates for the solution of this equation. |
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