A sharp estimate for the HardyLittlewood maximal function
Abstract
The best constant in the usual Lp norm inequality for the centered HardyLittlewood maximal function on R1 is obtained for the class of all ``peakshaped'' functions. A positive function on the line is called ``peakshaped'' if it is positive and convex except at one point. The techniques we use include convexity and an adaptation of the standard EulerLangrange variational method.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 1997
 DOI:
 10.48550/arXiv.math/9704211
 arXiv:
 arXiv:math/9704211
 Bibcode:
 1997math......4211G
 Keywords:

 Mathematics  Functional Analysis;
 42B25
 EPrint:
 Also available at http://www.math.missouri.edu/~stephen/preprints/