The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory

General H-function of two variables and the solution of its convergence problem main properties, series presentations and characteristic of the H-function H-function with the third characteristic and its particular cases G-function of two variables table of special cases of the G-function one-dimensional H-transform in spaces -1(L) and -1c,gamma(L) and its composition structure classical Laplace convolution and its new properties general integral convolution for H-function transform existence and factorization property of the convolution new examples of convolution for classical integral transforms generalized integral convolution general Leibniz rules and their integral analogs.