Abstract

Let \(t\in(0,\infty)\), \(\vec{p}\in(1,\infty)^{n}\) and \(\vec{q}\in[1,\infty)^{n}\). We establish versions of the Rubio de Francia extrapolation theorem, and further obtain the bounds for some classical operators and the commutators in harmonic analysis on the mixed-norm amalgam space \((L^{\vec{p}},L^{\vec{q}})_{t}({\mathbb{R}^{n}})\). As an application, a characterization of the mixed-norm amalgam spaces is given.

中文翻译：

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通过外推法对混合范数汞齐空间进行算子

摘要

设\(t\in(0,\infty)\)、\(\vec{p}\in(1,\infty)^{n}\)和\(\vec{q}\in[1,\ infty)^{n}\)。我们建立了 Rubio de Francia 外推定理的版本，并进一步得到了混合范数汞齐空间上调和分析中一些经典算子和交换子的界限 \((L^{\ vec{p}},L^{\ vec{q}})_{t}({\mathbb{R}^{n}})\)。作为一个应用，给出了混合范数汞齐空间的表征。