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In this chapter the principal aim is to establish boundedness and invertibility results for boundary layer potentials associated with weakly elliptic systems in the context of Beurling-Hardy spaces HAp and spaces of functions of bounded central mean oscillations BCMOp. This is possible thanks to the Calderón-Zygmund theory for singular integral operators developed in Chapter 6. The invertibility results obtained here play a decisive role in the treatment of boundary value problems in AR domains and boundary data selected from HAp spaces and BCMOp spaces (see Chapter 9).

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Layer Potentials on Beurling-Hardy Spaces and BCMOp Spaces

  • 章节

  • 发表日期：

    2026年

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  • Marius Mitrea,
  • Pedro Takemura

摘要

In this chapter the principal aim is to establish boundedness and invertibility results for boundary layer potentials associated with weakly elliptic systems in the context of Beurling-Hardy spaces HAp and spaces of functions of bounded central mean oscillations BCMOp. This is possible thanks to the Calderón-Zygmund theory for singular integral operators developed in Chapter 6. The invertibility results obtained here play a decisive role in the treatment of boundary value problems in AR domains and boundary data selected from HAp spaces and BCMOp spaces (see Chapter 9).