Some remarks on the $L^p-L^q$ boundedness  of trigonometric sums and oscillatory integrals

Damiano Foschi

doi:10.3934/cpaa.2005.4.569

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2005, Volume 4, Issue 3: 569-588. Doi: 10.3934/cpaa.2005.4.569

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Some remarks on the $L^p-L^q$ boundedness of trigonometric sums and oscillatory integrals

Damiano Foschi^1,

1.
Dipartimento di Matematica Pura e Applicata, Università di L'Aquila, 67100 Coppito

Received: September 2004

Revised: February 2005

Published: September 2005

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Abstract

We discuss the asymptotic behaviour for the best constant in $L^p$-$L^q$ estimates for trigonometric polynomials and for an integral operator which is related to the solution of inhomogeneous Schrödinger equations. This gives us an opportunity to review some basic facts about oscillatory integrals and the method of stationary phase, and also to make some remarks in connection with Strichartz estimates.

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Mathematics Subject Classification: Primary 26D15; Secondary 42A05.

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