A weighted theory for multilinear fractional integral operators and maximal functions is presented. Sufficient conditions for the two weight inequalities of these operators are found, including “power and logarithmic bumps” and anA _∞ condition. For one weight inequalities a necessary and sufficient condition is then obtained as a consequence of the two weight inequalities. As an application, Poincaré and Sobolev inequalities adapted to the multilinear setting are presented.

中文翻译：

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多线性分数积分算子的加权不等式

提出了多线性分数积分算子和最大函数的加权理论。对于这些操作符的两个权不等式充分条件被发现，其中“功率和对数凸块”和甲 _∞条件。对于一个重量不等式，由于两个重量不等式，因此获得了必要的充分条件。作为应用，提出了适用于多线性设置的庞加莱和Sobolev不等式。