The density of the area integral for parabolic functions is defined in analogy with the case of harmonic functions. We prove its equivalence with the local time of the associated martingale. Using probabilistic methods, we show its equivalence in L p -norm with the parabolic area function for p>1.
@article{urn:eudml:doc:41693,
title = {A note on the density of the parabolic area integral.},
journal = {Collectanea Mathematica},
volume = {52},
year = {2001},
pages = {75-84},
zbl = {0986.60070},
mrnumber = {MR1833087},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41693}
}
Iribarren, Ileana. A note on the density of the parabolic area integral.. Collectanea Mathematica, Tome 52 (2001) pp. 75-84. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41693/