## Maximal averages over flat radial hypersurfaces.(English)Zbl 0961.42015

Consider the operator $Af := \sup_{t > 0} f * d\sigma_t$ where $$d\sigma_t$$ is a normalized surface measure on some smooth compact hypersurface $$tS$$. If this surface has finite type then this operator is bounded on a non-trivial range of $$L^p$$. The author studies the infinite type case, in which one can only expect Orlicz space estimates. In the case when the surface is a surface of revolution the author obtains essentially sharp criteria on the Orlicz spaces on which A is bounded.

### MSC:

 42B25 Maximal functions, Littlewood-Paley theory 53A05 Surfaces in Euclidean and related spaces
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