naa a22 4500 510811051 CHVBK 20180411083442.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s12220-011-9256-2 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9256-2 Gressman Philip David Rittenhouse Lab, 209 South 33rd Street, 19104, Philadelphia, PA, USA aut Uniform Sublevel Radon-like Inequalities [Elektronische Daten] [Philip Gressman] This paper is concerned with establishing uniform weighted L p -L q 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 L p -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. Mathematica Josephina, Inc., 2011 Radon-like transforms nationallicence Sublevel set operators nationallicence Affine-invariant inequalities nationallicence Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 611-652 1050-6926 23:2<611 2013 23 12220 https://doi.org/10.1007/s12220-011-9256-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9256-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gressman Philip David Rittenhouse Lab, 209 South 33rd Street, 19104, Philadelphia, PA, USA aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 611-652 1050-6926 23:2<611 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer