The convolution for zero-order Mehler-Fock transform and pseudo-differential operator

The main aim of this paper is to find out the estimates of convolution for zero-order Mehler-Fock transform with various approaches. Pseudo-differential operator in terms of zero-order Mehler-Fock transform is defined and obtained its another integral representation. Further, its estimate in Lebesgue space has been studied. At the end some applications of zero-order Mehler-Fock transform and of convolution are discussed.