A+ CATEGORY SCIENTIFIC UNIT

$\Psi $-pseudodifferential operators and estimates for maximal oscillatory integrals

Volume 183 / 2007

Carlos E. Kenig, Wolfgang Staubach Studia Mathematica 183 (2007), 249-258 MSC: Primary 35S05; Secondary 42B20, 42B20. DOI: 10.4064/sm183-3-3

Abstract

We define a class of pseudodifferential operators with symbols $a(x,\xi )$ without any regularity assumptions in the $x$ variable and explore their $L^{p}$ boundedness properties. The results are applied to obtain estimates for certain maximal operators associated with oscillatory singular integrals.

Authors

  • Carlos E. KenigDepartment of Mathematics
    University of Chicago
    5734 South University Avenue
    Chicago, IL 60637, U.S.A.
    e-mail
  • Wolfgang StaubachDepartment of Mathematics
    Heriot-Watt University
    Colin Maclaurin Building
    Edinburgh, EH14 4AS, UK
    e-mail

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