# Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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## On parabolic measures and subparabolic functionsHTML articles powered by AMS MathViewer

by Jang Mei G. Wu
Trans. Amer. Math. Soc. 251 (1979), 171-185 Request permission

Erratum: Trans. Amer. Math. Soc. 259 (1980), 636-636.

## Abstract:

Let D be a domain in $R_x^n \times R_t^1$ and ${\partial _p}D$ be the parabolic boundary of D. Suppose ${\partial _p}D$ is composed of two parts B and S: B is given locally by $t = \tau$ and S is given locally by the graph of ${x_n} = f({x_1},{x_2}, \cdots ,{x_{n - 1}},t)$ where f is Lip 1 with respect to the local space variables and Lip $\tfrac {1} {2}$ with respect to the universal time variable. Let $\sigma$ be the n-dimensional Hausdorff measure in ${R^{n + 1}}$ and $\sigma ’$ be the $(n - 1)$-dimensional Hausdorff measure in ${\textbf {R}^n}$. And let $dm(E) = d\sigma (E \cap B) + d{\sigma ’} \times dt(E \cap S)$ for $E \subseteq {\partial _p}D$. We study (i) the relation between the parabolic measure on ${\partial _p}D$ and the measure dm on ${\partial _p}D$ and (ii) the boundary behavior of subparabolic functions on D.
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• Retrieve articles in Transactions of the American Mathematical Society with MSC: 31C99, 31D05, 35K99
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• Journal: Trans. Amer. Math. Soc. 251 (1979), 171-185
• MSC: Primary 31C99; Secondary 31D05, 35K99
• DOI: https://doi.org/10.1090/S0002-9947-1979-0531974-X
• MathSciNet review: 531974