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Journal of Function Spaces and Applications
Volume 2012, Article ID 792763, 21 pages
http://dx.doi.org/10.1155/2012/792763
Research Article

Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces

1Département de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405 Orsay, France
2School of Mathematics, Trinity College, Dublin 2, Ireland

Received 24 October 2011; Accepted 20 February 2012

Academic Editor: Miroslav Englis

Copyright ยฉ 2012 Stรฉphane Charpentier and Benoรฎt Sehba. 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 characterize those measures ๐œ‡ for which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) space ๐ปฮจ1 (resp., ๐ดฮจ1๐›ผ) of the unit ball of โ„‚๐‘ embeds boundedly or compactly into the Orlicz space ๐ฟฮจ2(๐”น๐‘,๐œ‡) (resp., ๐ฟฮจ2(๐”น๐‘,๐œ‡)), when the defining functions ฮจ1 and ฮจ2 are growth functions such that ๐ฟ1โŠ‚๐ฟฮจ๐‘— for ๐‘—โˆˆ{1,2}, and such that ฮจ2/ฮจ1 is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators from ๐ปฮจ1 (resp., ๐ดฮจ1๐›ผ) into ๐ปฮจ2 (resp., ๐ดฮจ2๐›ผ).