Sufficient conditions for the boundedness of the Hausdorff operators in the Hardy spaces , 0 < p < 1, on the real line are proved. Two related negative results are also given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-3-4,
author = {Elijah Liflyand and Akihiko Miyachi},
title = {Boundedness of the Hausdorff operators in $H^{p}$ spaces, 0 < p < 1},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {279-292},
zbl = {1184.42002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-3-4}
}
Elijah Liflyand; Akihiko Miyachi. Boundedness of the Hausdorff operators in $H^{p}$ spaces, 0 < p < 1. Studia Mathematica, Tome 192 (2009) pp. 279-292. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-3-4/