Geodesic
$\Psi $-pseudodifferential operators and estimates for maximal oscillatory integrals
Carlos E. Kenig 1   ; Wolfgang Staubach 2
1 Department of Mathematics University of Chicago 5734 South University Avenue Chicago, IL 60637, U.S.A.
2 Department of Mathematics Heriot-Watt University Colin Maclaurin Building Edinburgh, EH14 4AS, UK
Studia Mathematica, Tome 183 (2007) no. 3, pp. 249-258 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm183-3-3
Keywords: define class pseudodifferential operators symbols without regularity assumptions variable explore their boundedness properties results applied obtain estimates certain maximal operators associated oscillatory singular integrals

Carlos E. Kenig  1   ; Wolfgang Staubach  2

1 Department of Mathematics University of Chicago 5734 South University Avenue Chicago, IL 60637, U.S.A.
2 Department of Mathematics Heriot-Watt University Colin Maclaurin Building Edinburgh, EH14 4AS, UK 
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     title = {$\Psi $-pseudodifferential operators and estimates for
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 maximal oscillatory integrals
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Carlos E. Kenig; Wolfgang Staubach. $\Psi $-pseudodifferential operators and estimates for
 maximal oscillatory integrals. Studia Mathematica, Tome 183 (2007) no. 3, pp. 249-258. doi: 10.4064/sm183-3-3

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