The Calderón-Zygmund theory for singular integral operators on Beurling-Hardy spaces and the space of bounded central mean oscillation functions opens the door for employing boundary layer potential techniques for treating boundary problems on these scales. This chapter is devoted to studying the Neumann Problem with boundary data prescribed in HAp and the Dirichlet Problem with boundary data prescribed in BCMOp for second-order homogeneous constant complex coefficient weakly elliptic systems in δ-AR domains, with δ ∈ (0, 1) sufficiently small.

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Boundary Value Problems on HAp Spaces and BCMOp Spaces

  • Marius Mitrea,
  • Pedro Takemura

摘要

The Calderón-Zygmund theory for singular integral operators on Beurling-Hardy spaces and the space of bounded central mean oscillation functions opens the door for employing boundary layer potential techniques for treating boundary problems on these scales. This chapter is devoted to studying the Neumann Problem with boundary data prescribed in HAp and the Dirichlet Problem with boundary data prescribed in BCMOp for second-order homogeneous constant complex coefficient weakly elliptic systems in δ-AR domains, with δ ∈ (0, 1) sufficiently small.