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\({\mathbf {L}}^{{\mathbf {p}}}\)-Sobolev Estimates for a Class of Integral Operators with Folding Canonical Relations

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Abstract

We prove a sharp \(L^p\)-Sobolev regularity result for a class of generalized Radon transforms for families of curves in a three-dimensional manifold, with folding canonical relations. The proof relies on decoupling inequalities by Wolff and by Bourgain–Demeter for plate decompositions of thin neighborhoods of cones.

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Acknowledgements

The authors thank Geoffrey Bentsen for reading a draft of this paper and providing valuable input.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Room 121, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

    Malabika Pramanik

  2. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Andreas Seeger

Authors
  1. Malabika Pramanik
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  2. Andreas Seeger
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Correspondence to Andreas Seeger.

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In memory of Eli Stein.

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Supported in part by NSERC and NSF grants.

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Pramanik, M., Seeger, A. \({\mathbf {L}}^{{\mathbf {p}}}\)-Sobolev Estimates for a Class of Integral Operators with Folding Canonical Relations. J Geom Anal 31, 6725–6765 (2021). https://doi.org/10.1007/s12220-020-00388-0

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  • DOI: https://doi.org/10.1007/s12220-020-00388-0

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