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In this paper, we study weighted inequalities for multilinear fractional maximal operators and fractional integrals. We prove sharp weighted Lebesgue space estimates for both operators when the vector of weights belongs to [ABSTRACT FROM AUTHOR]

Abstract: We give several characterizations multiparameter in terms of strong maximal functions, rectangular conjugate functions, and rectangular partial sums. We also define a way to enumerate that corresponds to rectangles. We then use these enumerations to give another characterization of rectangular in terms of trigonometric Schauder bases. Finally, we present some applications to principle shift invariant spaces and Gabor systems. [Copyright &y& Elsevier]

Abstract: The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities. [Copyright &y& Elsevier]