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In this chapter we introduce and study the space of functions of (p, q)-bounded central mean oscillations BCMOp,q on unbounded Ahlfors regular sets, which extends the scale of bounded central p-mean oscillations functions BCMOp discussed in Chapter 5. We begin by establishing some basic functional analytic properties of BCMOp,q, with the ultimate goal of proving that the dual of first-generation Herz-type Hardy spaces HAp,q coincides with BCMOp′ ,q modulo constants.

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Functions of (p, q)-Bounded Central Mean Oscillations

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  • 发表日期：

    2026年

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  • Marius Mitrea,
  • Pedro Takemura

摘要

In this chapter we introduce and study the space of functions of (p, q)-bounded central mean oscillations BCMOp,q on unbounded Ahlfors regular sets, which extends the scale of bounded central p-mean oscillations functions BCMOp discussed in Chapter 5. We begin by establishing some basic functional analytic properties of BCMOp,q, with the ultimate goal of proving that the dual of first-generation Herz-type Hardy spaces HAp,q coincides with BCMOp′ ,q modulo constants.