A translation-invariant Banach space is constructed on which the non-classical maximal operator M^diamond is bounded but the sharp maximal operator M^sharp is not.
Rubio de Francia.Weighted norm inequalities and related topics, volume 116 ofNorth-Holland Mathematics Studies
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A survey of conjectures and results on spherical maximal functions emphasizing problems with fractal dilation sets.
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A Banach space that distinguishes two maximal operators
A translation-invariant Banach space is constructed on which the non-classical maximal operator M^diamond is bounded but the sharp maximal operator M^sharp is not.
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Problems on spherical maximal functions
A survey of conjectures and results on spherical maximal functions emphasizing problems with fractal dilation sets.