单位球上F(p,q,s)空间的分解和刻画

肖建斌, 张学军, 尚清丽, 郭雨婷

数学学报 ›› 2018, Vol. 61 ›› Issue (6) : 1037-1048.

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数学学报 ›› 2018, Vol. 61 ›› Issue (6) : 1037-1048. DOI: 10.12386/A2018sxxb0094
论文

单位球上F(p,q,s)空间的分解和刻画

    肖建斌1, 张学军2, 尚清丽2, 郭雨婷2
作者信息 +

Decomposition and Characterization of the F(p,q,s) Space on the Unit Ball

    Jian Bin XIAO1, Xue Jun ZHANG2, Qing Li SHANG2, Yu Ting GUO2
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文章历史 +

摘要

p>0,s ≥ 0,q>max{-n-1,-s-1},本文探讨了单位球上Fp,q,s)空间的一种等价刻画和分解问题.具体结果为:(1) fFp,q,s)当且仅当fHB),且Ip=supaBB|Rα,γfz)|p(1-|z|2q+pγ-p(1-|φaz)|2sdvz)<∞,其中α>-1 和γ>max{0,1-(q+s+1)/p,1-(q+n+1)/p}. (2) 若{dk}∈ ∫p,则存在序列{wk}⊂B,使得 fz)=∑k=1dk(1-|wk|2t+1)/(1-<zwk>)t+(q+n+1)/p)(zB)属于Fp,q,s),其中t>max{1-1/p,0}(q+n+1)+max{1/p,1}s-1.

Abstract

Let p > 0, s ≥ 0, q > max{-n-1, -s -1}. In this paper, the authors discuss an equivalent characterization and a decomposition of the F(p,q,s) space on the unit ball. The results as follows:(1) fF(p,q,s) if and only if fH(B) and Ip=supaBB|Rαf(z)|p(1 -|z|2)q+pγ-p(1 -|?a(z)|2)sdv(z) < ∞, where α > -1 and γ > max{0,1 -(q +s+1)/p,1 -(q + n+1)/p}. (2) If {dk} ∈ ∫p, then there exists sequence {wk} ⊂B such that f(z)=∑k=1(dk(1-|wk|2)t+1)/((1-<z,wk>)t+((q+n+1)/p)) (zB) in F(p,q,s), where t > max{1 -1/p,0}(q + n + 1) + max{1/p,1}s -1.

关键词

F(p / q / s)空间 / 等价刻画 / 原子分解 / 单位球

Key words

F(p,q,s) space / equivalent characterization / atomic decomposition / unit ball

引用本文

导出引用
肖建斌, 张学军, 尚清丽, 郭雨婷. 单位球上F(p,q,s)空间的分解和刻画. 数学学报, 2018, 61(6): 1037-1048 https://doi.org/10.12386/A2018sxxb0094
Jian Bin XIAO, Xue Jun ZHANG, Qing Li SHANG, Yu Ting GUO. Decomposition and Characterization of the F(p,q,s) Space on the Unit Ball. Acta Mathematica Sinica, Chinese Series, 2018, 61(6): 1037-1048 https://doi.org/10.12386/A2018sxxb0094

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基金

国家自然科学基金资助项目(11571104)

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