单位球上F(p,q,s)空间的分解和刻画
Decomposition and Characterization of the F(p,q,s) Space on the Unit Ball
设p>0,s ≥ 0,q>max{-n-1,-s-1},本文探讨了单位球上F(p,q,s)空间的一种等价刻画和分解问题.具体结果为:(1) f∈ F(p,q,s)当且仅当f∈ H(B),且Ip=supa∈B∫B|Rα,γf(z)|p(1-|z|2)q+pγ-p(1-|φa(z)|2)sdv(z)<∞,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 f(z)=∑k=1∞(dk(1-|wk|2)t+1)/(1-<z,wk>)t+(q+n+1)/p)(z∈B)属于F(p,q,s),其中t>max{1-1/p,0}(q+n+1)+max{1/p,1}s-1.
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) f ∈ F(p,q,s) if and only if f ∈ H(B) and Ip=supa∈B∫B|Rα,γf(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)) (z ∈ B) in F(p,q,s), where t > max{1 -1/p,0}(q + n + 1) + max{1/p,1}s -1.
F(p / q / s)空间 / 等价刻画 / 原子分解 / 单位球 {{custom_keyword}} /
F(p,q,s) space / equivalent characterization / atomic decomposition / unit ball {{custom_keyword}} /
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国家自然科学基金资助项目(11571104)
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