The Ergodic Maximal Function with Cancellation
Jones, Roger L.
Ann. Probab., Tome 4 (1976) no. 6, p. 91-97 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
A variant of the ergodic maximal function is studied. This maximal function reduces to the usual one for $f \geqq 0$, but the cancellation between the positive and negative parts of $f$ causes interesting behavior. In particular the maximal function can be in $L^1$ even when the function is not in $L \log^+ L$. A relation between this maximal function and the ergodic Hilbert transform is studied.
Publié le : 1976-02-14
Classification:  Maximal functions,  Hilbert transform,  ergodic theory,  measure preserving transformations,  flows,  $H^1$,  $L \log^+ L$,  28A65,  42A40,  42A36 
@article{1176996184,
     author = {Jones, Roger L.},
     title = {The Ergodic Maximal Function with Cancellation},
     journal = {Ann. Probab.},
     volume = {4},
     number = {6},
     year = {1976},
     pages = { 91-97},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996184}
}

Jones, Roger L. The Ergodic Maximal Function with Cancellation. Ann. Probab., Tome 4 (1976) no. 6, pp.  91-97. http://gdmltest.u-ga.fr/item/1176996184/