VAN DER CORPUT LEMMA WITH BESSEL FUNCTIONS

In this article, we study analogues of the van der Corput lemmas [19] involving Bessel functions. harmonic analysis, one most important estimates is lemma, which an estimate oscillatory integrals. This was first obtained by Dutch mathematician Johannes Gaultherus Corput. Van interested in behavior for large positive λ integral R b a e iλφ(x)ψ(x)dx, where φ real-valued smooth function (the phase) and ψ complex valued (amplitude). case = −∞, +∞, it assumed that has compact support R. our replace exponential with functions, to integrals appearing analysis wave equation singular damping. More specifically, form I(λ) Jn(λφ(x))ψ(x)dx range n 0, ∈ C smooth, real number can vary.The generalisations lemma proved. As application above results, generalised Riemann-Lebesgue considered.