The present paper is devoted to the study of the Mehler-Fock transform with index as the Legendre function of first kind. Continuity property of the Mehler-fock transform on the test function spaces Λ α and G α is given. Moreover pseudo-differential operator (p.d.o.) with symbol σ (x, τ) ∈ S m in terms of Mehler-Fock transform is defined and also its continuity property from test function space G α into Λ α is shown. The Mehler-Fock potential (MF-potential) P s σ is defined on G α (I) space and it is extended to the space of distribution. Also some properties of MF-potential are discussed. At the end Sobolev type space V s,p (I) is defined and it is shown that MF-potential is an isometry of V s,p (I).