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S. Butler and J. Rosenblatt
Growth of maximal functions view print
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| Published: |
July 9, 2012 |
| Keywords: |
Maximal functions, maximal inequalities, Lebesgue derivatives, ergodic averages |
| Subject: |
42B25, 28D05, 37A05 |
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Abstract
We consider the integrability of ϕ(f*) for various
maximal functions f* and various increasing functions ϕ.
We show that for some of the standard maximal functions arising in harmonic
analysis and ergodic theory, there is never integrability of
ϕ(f*) for all Lebesgue integrable functions f except
in cases where the growth of ϕ is slow enough so that
the integrability follows from the standard weak maximal
inequalities.
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| Acknowledgements
The second author was partially supported by NSF grant DMS 0555905
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| Author information
Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, 1409 West Green Street, Urbana, IL 61801, USA
svbutler@illinois.edu
rosnbltt@illinois.edu
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