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 $ \gamma =\sin y $ 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 $ L_p $ L p 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 $ L_1 $ L 1 space are also founded. [ABSTRACT FROM AUTHOR]