L p ′ ESTIMATES FOR OVERDETERMINED RADON TRANSFORMS

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【标题】L p ′ ESTIMATES FOR OVERDETERMINED RADON TRANSFORMS

【作者】 RADON TRANSFORMS  Luca Brandolini  Allan Greenleaf 

【摘要】We prove several variations on the results in [RT] (F. Ricci and G. Travaglini; Proc. A.M.S. 129(2001);1739–1744) concerning Lp ? Lp bounds for convolution with all rotations of arc length measure on a fixed convex curve in R2. Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces; smooth k-dimensional surfaces; and nontranslationinvariant families of surfaces. We compare the approach of [RT]; based on average decay of the Fourier transform; with an approach based on L2 boundedness of Fourier integral operators; and show that essentially the same geometric condition arises in proofs using the two techniques. §

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