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