Parabolic Potential Theory (Continued)

  • Joseph L. Doob
Part of the Classics in Mathematics book series (CLASSICS)

Abstract

If Ḋ is a nonempty open subset of ℝ̇ N and if Γ is a class of functions on Ḋ, the greatest subparabolic minorant [least superparabolic majorant] of Γ, if there is one, is denoted by ĠMΓ [ĿMΓ]. For example, if Γ is a class of superparabolic functions and if Γ has a subparabolic minorant then ĠMΓ exists and is parabolic. The proof is a translation of that of Theorem III.2. The corresponding notation in the coparabolic context is \( \mathop{G}\limits^{*} {M_{{\mathop{D}\limits^{.} }}}\Gamma \) and \( \mathop{L}\limits^{*} {M_{{\mathop{D}\limits^{.} }}}\Gamma \).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Joseph L. Doob
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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