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Journal of Function Spaces
Volume 2014, Article ID 234790, 9 pages
http://dx.doi.org/10.1155/2014/234790
Research Article

Spaces on the Unit Circle

School of Sciences, Anhui University of Science and Technology, Huainan, Anhui 232001, China

Received 11 May 2014; Accepted 28 July 2014; Published 20 August 2014

Academic Editor: Jose Luis Sanchez

Copyright © 2014 Jizhen Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a new space of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on such that , as well as a general criterion on weight functions and , , such that . We also prove that a measurable function belongs to if and only if it is Möbius bounded in the Sobolev space . Finally, we obtain a dyadic characterization of functions in spaces in terms of dyadic arcs on the unit circle.