Trigonometric weighted generalized convolution operator associated with Fourier cosine–sine and Kontorovich–Lebedev transformations

The main objective of this work is to introduce the generalized convolution with trigonometric weighted γ=sin⁡y involving the Fourier cosine–sine and Kontorovich–Lebedev transforms, and to study its fundamental results. We establish the boundedness properties in a two-parametric family of Lebesgue spaces for this convolution operator. Norm estimation in the weighted Lp space is obtained and applications of the corresponding class of convolution integro-differential equations are discussed. The conditions for the solvability of these equations in L1 space are also founded.