Uniform convergence of double trigonometric integrals

Abstract

We study the uniform convergence of double cosine integrals, sine-cosine integrals and double sine integrals of double general monotone functions. We extend the results of F. Móricz and of A. Debernardi concerning the uniform convergence of double sine integrals and the results of M. Dyachenko, E. Liflyand and S. Tikhonov regarding the uniform convergence of single trigonometric integrals.