## Generalized local Fatou theorems and area integrals

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- by B. A. Mair, Stan Philipp and David Singman PDF
- Trans. Amer. Math. Soc.
**321**(1990), 401-413 Request permission

## Abstract:

Let $X$ be a space of homogeneous type and $W$ a subset of $X \times (0,\infty )$. Then, under minimal conditions on $W$, we obtain a relationship between two modes of convergence at the boundary $X$ for functions defined on $W$. This result gives new local Fatou theorems of the Carleson-type for solutions of Laplace, parabolic and Laplace-Beltrami equations as immediate consequences of the classical results. Lusin area integral characterizations for the existence of limits within these more general approach regions are also obtained.## References

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## Additional Information

- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**321**(1990), 401-413 - MSC: Primary 31B25
- DOI: https://doi.org/10.1090/S0002-9947-1990-0974520-3
- MathSciNet review: 974520