PDF(464 KB)
PDF(464 KB)
PDF(464 KB)
带多项式相位的高维振荡积分算子的有界性
The Boundedness for an Oscillatory Integral Operator on Multi-dimension with Polynomial Phase
考虑如下的振荡积分算子：
中函数f为定义在Rn上的Schwartz函数，并且满足m，k>0.本文给出算子Tm，k，n从Lp（Rn）（1 ≤ p < ∞）到Lq（Rn）有界的一个充分必要条件.此外，我们还证明了算子Tm，k，n把L1（Rn）映到l0（Rn）.
We consider the following oscillatory integral operator:
where the function f is assumed to be a Schwartz function on Rn and m, k > 0. In this paper, we characterize the sufficient and necessary conditions which ensure the boundedness for Tm,k,n from Lp(Rn) (1 ≤ p < ∞) to Lq(Rn). In addition, the operator Tm,k,n also maps L1(Rn) into l0(Rn).
振荡积分算子 / 有界性 / Lp(Rn) {{custom_keyword}} /
oscillatory integral operator / boundedness / Lp(Rn) {{custom_keyword}} /
[1] Cheng L. C., Pan Y. B., Lp estimates for oscillatory integral operators, Proc. Amer. Math. Soc., 1999, 127:2995-3002.
[2] Grafakos L., Classical and Modern Fourier Analysis, China Machine Press, Beijing, 2005.
[3] Lv P., Shi Z. S. H., Yan D., Some remarks on the Fourier transform, Pan-Amer. Math. J., 2013, 23:99-112.
[4] Pan Y. B., Uniform estimates for oscillatory integral operators, J. Funct. Anal., 1991, 100:207-220.
[5] Pan Y. B., Sampson G., Szeptycki P., L2 and Lp estimates for oscillatory integrals and their extended domains, Stud. Math., 1997, 122:201-225.
[6] Phone D. H., Stein E. M., Hilbert integrals, singular integrals, and Randon transform I, Acta Math., 1986, 157:99-157.
[7] Phone D. H., Stein E. M., Models of degenerate Fourier integral operators and Radon transforms, Ann. Math., 1994, 140:703-722.
[8] Rudin W., Real and Complex Analysis, 3rd Ed., McGraw-Hill, Singapore, 1987.
[9] Sampson G., Estimates of oscillatory integrals, Rend. Circ. Mat. Palermo, 2001, 57:141-148.
[10] Sampson G., Lp estimates for a class of oscillatory integrals, Proc. Amer. Math. Soc., 2003, 131:2727-2732.
[11] Sampson G., Szeptycki P., The complete (Lp, Lp) mapping properities of some oscillatory integrals in several dimensions, Canad. J. Math., 2001, 53:1031-1056.
国家自然科学基金（11471309，11561062）；2018年河南省高等学校重点科研项目（18A110028）信阳师范学院"南湖学者奖励计划"青年项目；信阳师范学院博士科研启动项目（16030）
/
| 〈 |
|
〉 |
