QK Spaces on the Unit Circle. (20th August 2014)

• Record Type: Journal Article
• Authors: Zhou, Jizhen
• Other Names: Sanchez Jose Luis Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-08-20
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/234790
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We introduce a new spaceQ K ( ∂ D ) of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition onK such thatQ K ( ∂ D ) = BMO ( ∂ D ), as well as a general criterion on weight functionsK 1 andK 2, K 1 ≤ K 2, such thatQ K 1 ( ∂ D )  Q K 2 ( ∂ D ) . We also prove that a measurable function belongs toQ K ( ∂ D ) if and only if it is Möbius bounded in the Sobolev spaceL K 2 ( ∂ D ) . Finally, we obtain a dyadic characterization of functions inQ K ( ∂ D ) spaces in terms of dyadic arcs on the unit circle.