TY - JOUR
T1 - Transversal multilinear Radon-like transforms
T2 - Local and global estimates
AU - Bennett, J.
AU - Bez, N.
AU - Gutiérrez, S.
PY - 2013/1/1
Y1 - 2013/1/1
N2 - We prove local "L-improving" estimates for a class of multilinear Radon-like transforms satisfying a strong transversality hypothesis. As a consequence, we obtain sharp multilinear convolution estimates for measures supported on fully transversal submanifolds of Euclidean space of arbitrary dimension. Motivated by potential applications in diffraction tomography, we also prove global estimates for the same class of Radon-like transforms under a natural homogeneity assumption.
AB - We prove local "L-improving" estimates for a class of multilinear Radon-like transforms satisfying a strong transversality hypothesis. As a consequence, we obtain sharp multilinear convolution estimates for measures supported on fully transversal submanifolds of Euclidean space of arbitrary dimension. Motivated by potential applications in diffraction tomography, we also prove global estimates for the same class of Radon-like transforms under a natural homogeneity assumption.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84884144111&partnerID=8YFLogxK
U2 - 10.4171/RMI/739
DO - 10.4171/RMI/739
M3 - Article
AN - SCOPUS:84884144111
SN - 0213-2230
VL - 29
SP - 765
EP - 788
JO - Revista Matematica Iberoamericana
JF - Revista Matematica Iberoamericana
IS - 3
ER -