Abstract
If \( \dot{D} \) is a nonempty open subset of \( {{\dot{\mathbb{R}}}^{N}} \) and if Г is a class of functions on \( \dot{D} \), the greatest subparabolic minorant [least superparabolic majorant] of Г, if there is one, is denoted by \( \dot{G}{{M}_{{\dot{D}}}}\Gamma \left[ {\dot{L}{{M}_{{\dot{D}}}}\Gamma } \right] \). For example, if Г is a class of superparabolic functions and if Г has a subparabolic minorant then \( \dot{G}{{M}_{{\dot{D}}}}\Gamma \) exists and is parabolic. The proof is a translation of that of Theorem III.2. The corresponding notation in the coparabolic context is \( \mathop{{\text{G}}}\limits^{*} {{{\text{M}}}_{{\dot{D}}}}\Gamma \) and \( \mathop{{\text{L}}}\limits^{*} {{{\text{M}}}_{{\dot{D}}}}\Gamma \).
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© 1984 Springer-Verlag New York Inc.
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Doob, J.L. (1984). Parabolic Potential Theory (Continued). In: Classical Potential Theory and Its Probabilistic Counterpart. Grundlehren der mathematischen Wissenschaften, vol 262. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5208-5_17
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DOI: https://doi.org/10.1007/978-1-4612-5208-5_17
Publisher Name: Springer, New York, NY
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