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On Fourier Multipliers Over Tube Domains

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Recent Advances in Harmonic Analysis and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 25))

Abstract

We provide L p→L q estimates for a class of Fourier multipliers supported in convex cones of { R } n+1. In particular, we consider cones whose boundary has n−1 nonvanishing principal curvatures and cones which are the convex envelope of N linearly independent half lines passing through the origin of { R } n+1. In some case our estimates are best possible.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Florida International University, Miami, FL, USA

    Laura De Carli

Authors
  1. Laura De Carli
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Correspondence to Laura De Carli .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of South Carolina, Greene Street 1523, Columbia, 29208, South Carolina, USA

    Dmitriy Bilyk

  2. University Park, Department of Mathematics, Florida International University, SW 8th St., Rm 416 11200, Miami, 33199, Florida, USA

    Laura De Carli

  3. , Department of Mathematics, Universtity of Georgia, University of Georgia, Athens, 30602, Georgia, USA

    Alexander Petukhov

  4. Georgia Southern University, PO Box 8093, Statesboro, 30460, Georgia, USA

    Alexander M. Stokolos

  5. , Department of Mathematics, Georgia Institute of Technology, Cherry Street 686, Atlanta, 30332, Georgia, USA

    Brett D. Wick

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De Carli, L. (2012). On Fourier Multipliers Over Tube Domains. In: Bilyk, D., De Carli, L., Petukhov, A., Stokolos, A., Wick, B. (eds) Recent Advances in Harmonic Analysis and Applications. Springer Proceedings in Mathematics & Statistics, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4565-4_10

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