|
- 2015
分数阶截断算子的有界性
|
Abstract:
摘要 研究两类截断算子从 Lp 到 Lr 的有界性问题.需要指出的是, 对于某个固定的 p, 可得到 r的一个变化区间,刻画出这个区间与分数阶的关系. 此外,还给出算子范数上界的一个估计.
[1] | Lu S Z, Zhang Y. Criterion on <em>L</em><sup><i>p</i></sup> boundedness for a class of oscillatory singular integrals with rough kernels[J]. Rev. Mat. Iber., 1992(8): 201-219. |
[2] | Lu S Z, Yan D Y. Lp-boundedness of multilinear oscillatory singular integrals with Calderon-Zygmund kernel[J]. Science in China (Series A), 2002, 45(2): 196-213. |
[3] | Shi Z S, Yan D Y. Criterion on <em>L</em><sup>p<sub>1</sub></sup>×<em>L</em><sup>p<sub>2</sub></sup>→<em>L</em><sup>q</sup>-boundedness for oscillatory bilinear hilbert transform[J]. Abstract and Applied Analysis, Volume 2014, Article ID 712 051. |
[4] | 陆善镇,王昆阳.实分析[M].北京:北京师范大学出版社,2006. |
[5] | 丁勇. 现代分析基础[M]. 北京:北京师范大学出版社, 2008: 143-149. |
[6] | Stein E, Weiss G. Introduction to Fourier analysis on euclidean spaces[M]. Princeton University Press, Princeton, New Jersey, 1971: 53-75. |
[7] | Fernandez D. Vector-valued singular integral operators on Lp-spaces with mixed norms and applications[J]. Pacific J Math, 1987,129: 257-275. |
[8] | Stefanov A, Torres R. Calderón-Zygmund operators on mixed Lebesgue spaces and applications to null forms[J]. J London Math Soc, 2004,70(2): 447-462. |
[9] | Lu S Z, Ding Y, Yan D Y. Singular integral and related topics[M]. World Scientific Publishing Co Pte Ltd, 2007: 144-148. |
[10] | Grafakos L. Classical fourier analysis[M]. 2nd ed. Springer-Verlag, Graduate Texts in Mathematics 249, 2008: 77-82. |