The Kontorovich‐Lebedev transform and its associated pseudodifferential operator

In this paper, we obtained some useful estimates for convolution corresponding to Kontorovich‐Lebedev transform (KL‐transform) in Lebesgue space. Some continuity theorems for translation, convolution, and KL‐transform in test function space are discussed. Then an integral representation of pseudodifferential operator involving KL‐transform is found out, and its estimates in Lebesgue space is obtained. At the end, some applications of KL‐transform and its convolution are discussed.