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An $H^p$ scale for complete Pick spaces

Volume 258 / 2021

Alexandru Aleman, Michael Hartz, John E. M$^{\rm c}$Carthy, Stefan Richter Studia Mathematica 258 (2021), 343-359 MSC: Primary 46E22; Secondary 46B70, 47B35. DOI: 10.4064/sm200514-18-9 Published online: 9 December 2020


We define by interpolation a scale analogous to the Hardy $H^p$ scale for complete Pick spaces, and establish some of the basic properties of the resulting spaces, which we call $\mathcal {H}^p$. In particular, we obtain an $\mathcal {H}^p$-$\mathcal {H}^q$ duality and establish sharp pointwise estimates for functions in $\mathcal {H}^p$.


  • Alexandru AlemanMathematics
    Faculty of Science
    Lund University
    P.O. Box 118
    S-221 00 Lund, Sweden
  • Michael HartzFachrichtung Mathematik
    Universität des Saarlandes
    66123 Saarbrücken, Germany
  • John E. M$^{\rm c}$CarthyDepartment of Mathematics
    Washington University in St. Louis
    One Brookings Drive
    St. Louis, MO 63130, U.S.A.
  • Stefan RichterDepartment of Mathematics
    University of Tennessee
    1403 Circle Drive
    Knoxville, TN 37996-1320, USA

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