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/