Abstract We study the boundedness of the Hardy–Littlewood maximal operator in abstract extrapolation Banach function lattices and their Kothe dual spaces. The extrapolation spaces are generated by compatible families of Banach function lattices on quasi-metric measure spaces with doubling measure. These results combined with a variant of the integral Coifman–Fefferman inequality imply that every Calderon–Zygmund singular operator is bounded in considered extrapolation spaces. We apply these results to extrapolation spaces determined by compatible families of Calderon–Lozanovskii spaces, in particular to compatible families of Orlicz spaces that are interpolation of weighted L p -spaces ( 1 p ∞ ) with A p weights defined on spaces of homogeneous type.

中文翻译：

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外推空间中的 Calderón–Zygmund 奇异算子

摘要 我们研究了抽象外推 Banach 函数格及其 Kothe 对偶空间中 Hardy-Littlewood 极大算子的有界性。外推空间是由兼容的 Banach 函数格族在具有加倍测度的拟度量空间上生成的。这些结果与积分 Coifman-Fefferman 不等式的变体相结合，意味着每个 Calderon-Zygmund 奇异算子都在所考虑的外推空间中是有界的。我们将这些结果应用到由 Calderon-Lozanovskii 空间的兼容族确定的外推空间，特别是 Orlicz 空间的兼容族，它们是加权 L p 空间 ( 1 p ∞ ) 的插值，在齐次类型的空间上定义了 A p 权重。