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Analysis vs. geometry on a class of rectifiable hypersurfaces in $${\mathbb{R}}^ n$$. (English) Zbl 0699.42007
Indiana Univ. Math. J. (to appear)
This paper concerns the interaction between the geometry of rectifiable hypersurfaces in $${\mathbb{R}}^ n$$ and related analytical conditions. The author previously proved elsewhere that certain square function estimates hold for such a rectifiable hypersurface M under some simple geometric conditions. In this paper it is shown that these square function estimates can be used to obtain very strong control on the geometry of M, and that one can pass from this geometrical information to estimates for singular integral operators, and, under additional hypotheses, estimates for harmonic measure.
Reviewer: S.Semmes

##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory
##### Keywords:
square function; rectifiable hypersurface