The goal here is to develop a Calderón-Zygmund theory for singular integral operators on UR sets in the context of second-generation Herz-type Hardy spaces. This plays a crucial role in subsequent chapters as it allows us to employ boundary layer methods for treating boundary value problems with boundary data in \(\text{HK}_{p,q}^{\alpha }\) . We begin by studying principal value convolution-type SIO’s on \(\text{HK}_{p,q}^{\alpha }\) spaces.

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Singular Integral Operators on Herz-type Hardy Spaces of Second Generation

  • Marius Mitrea,
  • Pedro Takemura

摘要

The goal here is to develop a Calderón-Zygmund theory for singular integral operators on UR sets in the context of second-generation Herz-type Hardy spaces. This plays a crucial role in subsequent chapters as it allows us to employ boundary layer methods for treating boundary value problems with boundary data in \(\text{HK}_{p,q}^{\alpha }\) . We begin by studying principal value convolution-type SIO’s on \(\text{HK}_{p,q}^{\alpha }\) spaces.