标题： Muckenhoupt型条件在加权Morrey空间上 显示英文标题

标题： Muckenhoupt-type conditions on weighted Morrey spaces

摘要： 我们通过空间的Köthe对偶性在加权Morrey空间上定义了一种Muckenhoup型条件。 我们证明该条件是定义在以原点为中心的球上的最大算子在加权Morrey空间上有界性的必要且充分条件。 修改后的条件表征了Calderón算子的加权不等式。 我们还证明，Muckenhoup型条件对于通常的Hardy-Littlewood最大算子在加权局部Morrey空间上有界性是必要且充分的，从而简化了Nakamura-Sawano-Tanaka之前的表征。 对于同一算子，在全局Morrey空间的情况下，该条件是必要的，而为了充分性，我们增加了一个局部$A_p$条件。 我们可以在非常一般的设置中从Lebesgue$A_p$加权不等式外推到加权全局和局部Morrey空间，并应用于许多算子。 显示英文摘要

摘要： We define a Muckenhoup-type condition on weighted Morrey spaces using the K\"othe dual of the space. We show that the condition is necessary and sufficient for the boundedness of the maximal operator defined with balls centered at the origin on weighted Morrey spaces. A modified condition characterizes the weighted inequalities for the Calder\'on operator. We also show that the Muckenhoup-type condition is necessary and sufficient for the boundedness on weighted local Morrey spaces of the usual Hardy-Littlewood maximal operator, simplifying the previous characterization of Nakamura-Sawano-Tanaka. For the same operator, in the case of global Morrey spaces the condition is necessary and for the sufficiency we add a local $A_p$ condition. We can extrapolate from Lebesgue $A_p$-weighted inequalities to weighted global and local Morrey spaces in a very general setting, with applications to many operators.