## On parabolic measures and subparabolic functions

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- by Jang Mei G. Wu PDF
- 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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## Additional Information

- © Copyright 1979 American Mathematical Society
- 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