Discrete Analysis (Dec 2023)

Bi-parameter Potential theory and Carleson measures for the Dirichlet space on the bidisc

  • Nicola Arcozzi,
  • Pavel Mozolyako,
  • Karl-Mikael Perfekt,
  • Giulia Sarfatti

Abstract

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Bi-parameter potential theory and Carleson measures for the Dirichlet space on the bidisc, Discrete Analysis 2023:22, 58 pp. Carleson measures arise naturally when considering harmonic or holomorphic extensions from the boundary of a domain to the interior of the domain. For instance, suppose one has an $L^p$ function $f$ on the real line for some $1 \leq p