In this chapter we shall specialize the Calderón-Zygmund theory developed in Chapter 13 to boundary layer potentials in UR domains associated with second-order, homogeneous, constant complex coefficient, weakly elliptic systems. This is done in the context of first-generation Herz spaces, Herz-type Hardy spaces, and spaces of (p, q)-bounded central mean oscillations. The invertibility results obtained here play a decisive role later on in establishing solvability results for boundary problems sin the aforementioned function spaces.

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Layer Potentials on Herz-type Spaces of First Generation, and Invertibility Results

  • Marius Mitrea,
  • Pedro Takemura

摘要

In this chapter we shall specialize the Calderón-Zygmund theory developed in Chapter 13 to boundary layer potentials in UR domains associated with second-order, homogeneous, constant complex coefficient, weakly elliptic systems. This is done in the context of first-generation Herz spaces, Herz-type Hardy spaces, and spaces of (p, q)-bounded central mean oscillations. The invertibility results obtained here play a decisive role later on in establishing solvability results for boundary problems sin the aforementioned function spaces.