Two-weighted conditions and characterizations for a class of multilinear fractional new maximal operators

In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator M-phi,M-beta are established. Meanwhile, we introduce the S-((p) over right arrow ,S-q),S-beta(phi) and B-((p) over right arrow ,B-q),B-beta(phi) conditions and obtain the char-acterization of two-weighted inequalities for M-phi,M-beta. Finally, the relation-ships of the conditions S-(<(p)over (right arrow>,q),beta)(phi), A(((p) over right arrow ,q),beta)(phi) and B-((p) over right arrow ,B-q),B-beta(phi) and the characterization of the one-weight A(((p) over right arrow ,q),beta)(phi) are given.