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An oscillatory integral estimate associated to rational phases |
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| Authors: | |
| Institution: | (1) Instituto de Matemáticas, UNAM, Area de la Investigación Científica, Circuito Exterior, Ciudad Universitaria, 04510 México, D.F.;(2) School of Mathematics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, EH9 3JZ Edinburgh, Scotland |
| Abstract: | Let R(t)=P(t)/Q(t) be a quotient of real polynomials. We show that ∫exp(iR(t)) dt/t has a uniform bound with a bound depending only on the degrees of P and Q and not on their coefficients. Also LP estimates are obtained for certain associated singular integral operators. |
| Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 42B15 |
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