Rank and regularity for averages over submanifolds |
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Authors: | Philip T Gressman |
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Institution: | University of Pennsylvania, Mathematics Department, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia, PA 19104, United States |
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Abstract: | This paper establishes endpoint Lp-Lq and Sobolev mapping properties of Radon-like operators which satisfy a homogeneity condition (similar to semiquasihomogeneity) and a condition on the rank of a matrix related to rotational curvature. For highly degenerate operators, the rank condition is generically satisfied for algebraic reasons, similar to an observation of Greenleaf, Pramanik and Tang A. Greenleaf, M. Pramanik, W. Tang, Oscillatory integral operators with homogeneous polynomial phases in several variables, J. Funct. Anal. 244 (2) (2007) 444-487] concerning oscillatory integral operators. |
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Keywords: | Radon transform Oscillatory integral operator Rotational curvature |
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