The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation
Let B be the real unit ball in Rn and f∈CN(B). Given a multi-index m=(m1,…,mn) of nonnegative integers with |m|=N, we set the quantity supx∈B,y∈E(x,r),x≠y(1-|x|2)α(1-|y|2)β|∂mf(x)-∂mf(y)|/|x-y|γ[x,y]1-γ, x≠y, where 0≤γ≤1 and α+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces o...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/6814326 |
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doaj-466ad6bf68be4439a81ff035ca8a03862020-11-24T22:21:40ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/68143266814326The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an OscillationXi Fu0Zhiyao Xu1Xiaoyou Liu2Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, ChinaDepartment of Mathematics, Jiangxi Vocational College of Industry and Engineering, Pingxiang, Jiangxi 337055, ChinaSchool of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, ChinaLet B be the real unit ball in Rn and f∈CN(B). Given a multi-index m=(m1,…,mn) of nonnegative integers with |m|=N, we set the quantity supx∈B,y∈E(x,r),x≠y(1-|x|2)α(1-|y|2)β|∂mf(x)-∂mf(y)|/|x-y|γ[x,y]1-γ, x≠y, where 0≤γ≤1 and α+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting.http://dx.doi.org/10.1155/2016/6814326 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xi Fu Zhiyao Xu Xiaoyou Liu |
| spellingShingle |
Xi Fu Zhiyao Xu Xiaoyou Liu The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation Journal of Function Spaces |
| author_facet |
Xi Fu Zhiyao Xu Xiaoyou Liu |
| author_sort |
Xi Fu |
| title |
The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation |
| title_short |
The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation |
| title_full |
The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation |
| title_fullStr |
The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation |
| title_full_unstemmed |
The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation |
| title_sort |
harmonic bloch and besov spaces on the real unit ball by an oscillation |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2016-01-01 |
| description |
Let B be the real unit ball in Rn and f∈CN(B). Given a multi-index m=(m1,…,mn) of nonnegative integers with |m|=N, we set the quantity supx∈B,y∈E(x,r),x≠y(1-|x|2)α(1-|y|2)β|∂mf(x)-∂mf(y)|/|x-y|γ[x,y]1-γ, x≠y, where 0≤γ≤1 and α+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting. |
| url |
http://dx.doi.org/10.1155/2016/6814326 |
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