Optimal forward and reverse estimates of Morawetz and Kato-Yajima type with angular smoothing index (Q2342170)

The purpose of this paper is to find optimal bounds for integrals of the solutions of the Schrödinger equation, the wave equation, and the Klein-Gordon equation. The integrals of these solutions are bounded by certain parameters, which can depend on quotients of \(\Gamma\) functions. Tables of these constant parameters are given in a special case. The proofs use Stirlings formula, the logconvexity of the digamma function, mean value theorem, spherical harmonics, and Plancherels theorem. Finally, a generalization of the first estimate involving Bessel functions is given.