期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1973
卷号：70
期号：6
页码：1761-1763
DOI：10.1073/pnas.70.6.1761
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Suppose an ergodic flow acts on a probability space [M] enabling us to introduce the Ergodic Hilbert transform[IMG] f1.gif" ALT="f" BORDER="0"> of f [isin] Lp([M]), 1 [less double equals] p [less double equals] {infty}. H1 is the class of all functions of the form f + i[IMG]f1.gif" ALT="f" BORDER="0"> [isin] L1([M]). We show that H1 can be characterized in terms of a class of maximal functions; moreover, the dual space of H1 is identified with a space of functions of bounded mean oscillation defined in terms of the flow.
