Uniform Sublevel Radon-like Inequalities
Uniform Sublevel Radon-like Inequalities
复制标题
均匀子级类氡不等式
DOI：
10.1007/s12220-011-9256-2
复制
发表时间：
2010
影响因子：
1.1
通讯作者：
Philip T. Gressman
中科院分区：
文献类型：
--
作者：
Philip T. Gressman
This paper is concerned with establishing uniform weighted Lp–Lq estimates for a class of operators generalizing both Radon-like operators and sublevel set operators. Such estimates are shown to hold under general circumstances whenever a sublevel-type inequality is satisfied by certain associated measures (the inequality is of the sort studied by Oberlin (Math. Proc. Camb. Philos. Soc. 129(3):517–526, 2000), relating measures of parallelepipeds to powers of their Euclidean volumes). These ideas lead to previously unknown, weighted affine-invariant estimates for Radon-like operators as well as new Lp-improving estimates for degenerate Radon-like operators with folding canonical relations which satisfy an additional curvature condition of Greenleaf and Seeger (J. Reine Angew. Math. 455:35–56, 1994) for FIOs (building on the ideas of Sogge (Invent. Math. 104(2):349–376, 1991) and Mockenhaupt et al. (J. Am. Math. Soc. 6(1):65–130, 1993)); these new estimates fall outside the range of estimates which are known to hold in the generality of the FIO context.
