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

ABSTRACT

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 the 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.

KEYWORDS:

• Kontorovich–Lebedev transforms
• Fourier transforms
• convolution
• trigonometric weighted

AMS SUBJECT CLASSIFICATIONS:

• 42A38
• 44A15
• 44A35
• 45A05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research received no specific grant from any funding agency.