For all n≥3 and p>2, the strong spherical maximal operator is bounded on Lp, resolving the sharp n=3 case of the strong spherical maximal conjecture.
Spherical maximal estimates via geometry
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abstract
We present a simple geometric approach to studying the $L^p$ boundedness properties of Stein's spherical maximal operator, which does not rely on the Fourier transform. Using this, we recover a weak form of Stein's spherical maximal theorem.
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Improved $L^p$ bounds for the strong spherical maximal operator
For all n≥3 and p>2, the strong spherical maximal operator is bounded on Lp, resolving the sharp n=3 case of the strong spherical maximal conjecture.