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This chapter is primarily focused on developing a Calderón-Zygmund theory for second-generation Herz spaces on uniformly rectifiable sets. At the core of our approach one finds the interpolation result described in Theorem 17.3, the characterization obtained in Corollary 17.1, along with recently established results in the context of Muckenhoupt weighted Lebesgue spaces in [MMMi3]. The theory presented here is applicable to boundary layer potentials associated with weakly elliptic systems, which will be crucial in the treatment of boundary value problems on second-generation Herz spaces in subsequent chapters.

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Calderón-Zygmund Theory on Herz Spaces of Second Generation

  • 章节

  • 发表日期：

    2026年

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  • Marius Mitrea,
  • Pedro Takemura

摘要

This chapter is primarily focused on developing a Calderón-Zygmund theory for second-generation Herz spaces on uniformly rectifiable sets. At the core of our approach one finds the interpolation result described in Theorem 17.3, the characterization obtained in Corollary 17.1, along with recently established results in the context of Muckenhoupt weighted Lebesgue spaces in [MMMi3]. The theory presented here is applicable to boundary layer potentials associated with weakly elliptic systems, which will be crucial in the treatment of boundary value problems on second-generation Herz spaces in subsequent chapters.