Improved endpoint bounds for the lacunary spherical maximal operator

Abstract

We prove new endpoint bounds for the lacunary spherical maximal operator and as a consequence obtain almost everywhere pointwise convergence of lacunary spherical means for functions locally in $L\log \log \log L(\log \log \log \log L{)}^{1+\epsilon }$ for any $\epsilon >0$.

27 pages, 3 figures

Cited by in corpus (2)

• Lacunary Discrete Spherical Maximal Functions
• Lacunary Spherical Maximal Operators on Hyperbolic Spaces