Annals of Mathematical Sciences and Applications

Volume 6 (2021)

Number 1

A pair of Kontorovich–Lebedev type transforms and associated pseudo-differential operators

Pages: 87 – 118



U. K. Mandal (Department of Mathematics, Nalanda College, Patliputra University, Patna, India)

Akhilesh Prasad (Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, India)


In this paper, we have introduced Kontorovich–Lebedev type transform (KL-type transform) in two variables form, independent of index and further its two classifications are given. Differential operators associated to it is being introduced and further its continuity as well as of KL-type transforms on Zemanian type function spaces are discussed. Moreover, translation and convolution operator involving KL-type transform are given and in Lebesgue space their estimates are deduced. Furthermore, pseudo-differential operators associated to KL-type transforms are defined and on Zemanian type function spaces their continuity has been studied. Ultimately, an application of it has been shown by solving an integral equation.


Kontorovich–Lebedev transform, function spaces, pseudo-differential operator, convolution

2010 Mathematics Subject Classification

35S05, 44A20, 46F12

The second author is supported by Science and Engineering Research Board, Government of India, under Grant No. EMR/2016/005141.

Received 20 October 2020

Accepted 3 February 2021

Published 6 October 2021