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Revista Matemática Iberoamericana

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Volume 29, Issue 3, 2013, pp. 765–788
DOI: 10.4171/RMI/739

Published online: 2013-08-04

Transversal multilinear Radon-like transforms: local and global estimates

Jonathan Bennett[1], Neal Bez[2] and Susana Gutiérrez[3]

(1) University of Birmingham, UK
(2) University of Birmingham, Edgbaston, UK
(3) University of Birmingham, UK

We prove local “$L^p$-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.

Keywords: Multilinear forms, convolution estimates, diffraction tomography

Bennett Jonathan, Bez Neal, Gutiérrez Susana: Transversal multilinear Radon-like transforms: local and global estimates. Rev. Mat. Iberoam. 29 (2013), 765-788. doi: 10.4171/RMI/739