This paper gives an extension of the extrapolation theory to Herz spaces with variable exponents. By using this extrapolation theory, we establish the Fefferman–Stein inequalities, the Rubio de Francia inequalities, the John–Nirenberg inequalities, the characterizations of BMO and the boundedness of the geometrical maximal operator on Herz spaces with variable exponents.

中文翻译：

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用可变指数和应用外推到Herz空间

本文将外推理论扩展到具有可变指数的Herz空间。通过使用这种外推理论，我们建立了Fefferman-Stein不等式，Rubio de Francia不等式，John-Nirenberg不等式，BMO的刻画以及具有可变指数的Herz空间上的几何极大算子的有界性。