The topics treated in this chapter are as follows. In Section 17.1 we introduce the (homogeneous and inhomogeneous) measure theoretic Herz spaces and establish some of their basic functional analytic properties, while in Section 17.2 we show that this scale of spaces is stable under the real method of interpolation. In Section 17.3, we study second-generation Herz spaces in the context of unbounded Ahlfors regular sets.

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Measure Theoretic Herz Spaces

  • Marius Mitrea,
  • Pedro Takemura

摘要

The topics treated in this chapter are as follows. In Section 17.1 we introduce the (homogeneous and inhomogeneous) measure theoretic Herz spaces and establish some of their basic functional analytic properties, while in Section 17.2 we show that this scale of spaces is stable under the real method of interpolation. In Section 17.3, we study second-generation Herz spaces in the context of unbounded Ahlfors regular sets.