论文标题
加权莫雷空间上的Muckenhoupt型条件
Muckenhoupt-type conditions on weighted Morrey spaces
论文作者
论文摘要
我们使用该空间的双重双重的摩尔雷空间上定义了Muckenhoup型条件。我们表明，这种条件是必要且足够的，足以使最大算子的界限定义为以加权莫雷空间的原点为中心的球。修改后的条件表征了Calderón操作员加权不平等。我们还表明，对于通常强壮的木材最大操作员的加权局部莫雷空间的界限，Muckenhoup型条件是必要的，并且足够了，从而简化了Nakamura-Sawano-Tanaka的先前表征。对于同一操作员，对于全球摩尔岛空间，条件是必要的，对于充分性，我们添加了本地$ A_P $条件。我们可以在非常通用的环境中从Lebesgue $ a_p $加权的不平等现象推断出加权全球和本地的莫雷空间，并向许多运营商提供了应用。
We define a Muckenhoup-type condition on weighted Morrey spaces using the Köthe 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 Calderón 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.
