  The main objective of this work is to introduce the generalized convolution
with trigonometric weighted $\gamma=\sin y$ involving the Fourier cosine-sine
and Kontorovich-Lebedev transforms, and to study its fundamental results. We
establish boundedness properties in a two-parametric family of Lebesgue spaces
for this convolution operator. Norm estimation in the weighted $ 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 $L_1$ space are also founded.
