Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Abstract

Integral transforms of the form f(x)↦g(x)=(1−d2/dx2){∫0∞k1(y)[f(|x+y−1|)+f(|x−y+1|)−f(x+y+1)−f(|x−y−1|)]dy+∫0∞k2(y)[f(x+y)+f(|x−y|)]dy} from Lp(ℝ+) to Lq(ℝ+), (1≤p≤2,p−1+q−1=1) are studied. Watson's and Plancherel's theorems are obtained.