Hardy-Goldberg operator and its conjugate one in hardy spaces and BMO \((\mathbb{T})\)
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- 作者：S. S. Volosivets (1)
1. Saratov State University ; ul. Astrakhanskya 83 ; Saratov ; 410012 ; Russia - 关键词：Hardy ; Goldberg operator ; Lp space ; real Hardy space ; BMO ; VMO
- 刊名：Russian Mathematics (Iz VUZ)
- 出版年：2015
- 出版时间：February 2015
- 年：2015
- 卷：59
- 期：2
- 页码：14-24
- 全文大小：626 KB
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- 刊物主题：Mathematics
Mathematics
Russian Library of Science - 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
- ISSN：1934-810X
文摘
The Hardy operator is well-known in harmonic analysis. It transforms the sequence of Fourier coefficients of a function to a the sequence of its arithmetic means. In the paper we consider the Hardy-Goldberg operator generalizing the Hardy operator and its conjugate one. We prove the boundedness of the Hardy-Goldberg operator in the real Hardy space and of its analog in the Hardy space on the disc. We establish the boundedness of the conjugate Hardy-Goldberg operator in the periodic BMO andVMO spaces.