Selected Works of Donald L. Burkholder pp 199-216 | Cite as

# Distribution function inequalities for the area integral

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## Abstract

Let *A* be the area integral of a function *u* harmonic in the Euclidean half-space **R**^{n} x (0, ∞). Information about the distribution function of a localized version of *A* is obtained that leads to a general integral inequality between A and the nontangential maximal function of *u* and provides a convenient approach to the study of the pointwise behavior of *u* near the boundary. In addition, the general integral inequality of [2] between the nontangential maximal function of *u* and that of a properly chosen conjugate is shown to hold also in the case n > **1**.

## Keywords

Harmonic Function Boundary Point Maximal Function Lipschitz Domain Measurable Subset
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## References

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