Abstract
If Ḋ is a nonempty open subset of ℝ̇N 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 ĠMḊΓ [ĿMḊΓ]. For example, if Γ is a class of superparabolic functions and if Γ has a subparabolic minorant then ĠMḊΓ 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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© 2001 Springer-Verlag Berlin Heidelberg
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Doob, J.L. (2001). Parabolic Potential Theory (Continued). In: Classical Potential Theory and Its Probabilistic Counterpart. Classics in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56573-1_17
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DOI: https://doi.org/10.1007/978-3-642-56573-1_17
Publisher Name: Springer, Berlin, Heidelberg
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