September  2005, 4(3): 569-588. doi: 10.3934/cpaa.2005.4.569

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

1. 

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

Received  September 2004 Revised  February 2005 Published  June 2005

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.
Citation: Damiano Foschi. Some remarks on the $L^p-L^q$ boundedness of trigonometric sums and oscillatory integrals. Communications on Pure and Applied Analysis, 2005, 4 (3) : 569-588. doi: 10.3934/cpaa.2005.4.569
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