Transversal Multilinear Radon-like Transforms: Local and Global Estimates
نویسنده
چکیده
We prove local “Lp-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. We also prove global estimates for the same class of Radon-like transforms under a natural homogeneity assumption.
منابع مشابه
Multilinear generalized Radon transforms and point configurations
We study multilinear generalized Radon transforms using a graph-theoretic paradigm that includes the widely studied linear case. These provide a general mechanism to study Falconertype problems involving (k + 1)-point configurations in geometric measure theory, with k ≥ 2, including the distribution of simplices, volumes and angles determined by the points of fractal subsets E ⊂ Rd, d ≥ 2. If T...
متن کاملEstimates for Generalized Radon Transforms
Sobolev and L p ? L q estimates for degenerate Fourier integral operators with fold and cusp singularities are discussed. The results for folds yield sharp estimates for restricted X-ray transforms and averages over non-degenerate curves in R 3 and those for cusps give sharp L 2 estimates for restricted X-ray transforms in R 4. In R 4 , sharp Lebesgue space estimates are proven for a class of m...
متن کاملA Generalized Deconvolution Approach for Local Radon Transforms
A chief problem in seismic data processing is the filtering of unwanted events like ground roll and multiples. Methods to deal with this problem often exploit moveout or curvature differences between offending events and the events one would like to preserve (primaries). In particular, removal of multiples based on moveout discrimination can be attained via parabolic and hyperbolic Radon transf...
متن کاملDiscrete Analogues in Harmonic Analysis , I : ` 2 Estimates for Singular Radon Transforms
This paper studies the discrete analogues of singular Radon transforms. We prove the `2 boundedness for those operators that are “quasi-translation-invariant.” The approach used is related to the “circle-method” of Hardy and Littlewood, and requires multi-dimensional extensions of Weyl sums and Gauss sums, as well as variants that replace scalar sums by operator sums.
متن کاملMultilinear Estimates for Periodic Kdv Equations, and Applications
We prove an endpoint multilinear estimate for the X spaces associated to the periodic Airy equation. As a consequence we obtain sharp local well-posedness results for periodic generalized KdV equations, as well as some global well-posedness results below the energy norm.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011