Abstract: Because of. the great needs both for the research of pansystem mathematics andfor the analysis of general things’ mechanism, this paper discusses the binary relation,stransitivity confined to multirelation. The so-called g-transitvity- a completelynew concept about transitivity- is introduced and its basic properties are investigated.The study shows that it is not only g-transitivity a generalization of traditionaltransitivity, quasi-transitivity, seml-order, quasi-order and other panorder, but alsoincludes many important concepts such as closeness, convexity, topology, duality as itsspecial cases.

Key words: θ(t) -type singular integral operators, L^p_B(R^{n space,} H¹_B(Rⁿ) space, pansystems theory, relation panorder, order, transitivity, quasi-transitivity, g-transitivity