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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 also to make some remarks in connection with
Strichartz estimates.