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RISS 인기검색어
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- 저자 : Zengjian Lou (검색결과 4 건)
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On absolute values of ${\mathcal{Q}_K}$ functions
Guanlong Bao,Zengjian Lou,Ruishen Qian,Hasi Wulan 대한수학회 2016 대한수학회보 Vol.53 No.2
In this paper, the effect of absolute values on the behavior of functions $f$ in the spaces $\qk$ is investigated. It is clear that $g\in \qkt \Rightarrow |g|\in \qkt$, but the converse is not always true. For $f$ in the Hardy space $H^2$, we give a condition involving the modulus of the function only, such that the condition together with $|f|\in \qkt$ is equivalent to $f\in \qk$. As an application, a new criterion for inner-outer factorisation of $\qk$ spaces is given. These results are also new for $\qp$ spaces.
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Multipliers of Dirichlet-type subspaces of Bloch space
Songxiao Li,Zengjian Lou,Conghui Shen 대한수학회 2020 대한수학회보 Vol.57 No.2
Let $M(X,Y)$ denote the space of multipliers from $X$ to $Y,$ where $X$ and $Y$ are analytic function spaces. As we known, for Dirichlet-type spaces $\mathcal{D}_{\alpha}^p,$ $M(\mathcal{D}^p_{p-1},\mathcal{D}^q_{q-1})=\{0\},$ if $p\neq q,$ $0<p,q<\infty.$ If $0<p,q<\infty,$ $p\neq q,$ $0<s<1$ such that $p+s,q+s>1,$ then $M(\mathcal{D}^p_{p-2+s},\mathcal{D}^q_{q-2+s})=\{0\}.$ However, $X\cap\mathcal{D}^p_{p-1} \subseteq X\cap\mathcal{D}^q_{q-1}$ and $X\cap \mathcal{D}^p_{p-2+s} \subseteq X\cap \mathcal{D}^q_{q-2+s}$ whenever $X$ is a subspace of the Bloch space $\mathcal{B}$ and $0<p\leq q<\infty.$ This says that the set of multipliers $M(X\cap \mathcal{D}^p_{p-2+s},X\cap\mathcal{D}^q_{q-2+s})$ is nontrivial. In this paper, we study the multipliers $M(X\cap\mathcal{D}^p_{p-2+s},X\cap\mathcal{D}^q_{q-2+s})$ for distinct classical subspaces $X$ of the Bloch space $\mathcal{B},$ where $X=\mathcal{B},$ $BMOA$ or $\H^{\infty}.$
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MULTIPLIERS OF DIRICHLET-TYPE SUBSPACES OF BLOCH SPACE
Li, Songxiao,Lou, Zengjian,Shen, Conghui Korean Mathematical Society 2020 대한수학회보 Vol.57 No.2
Let M(X, Y) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlet-type spaces 𝓓<sub>α</sub><sup>p</sup>, M(𝓓<sub>p-1</sub><sup>p</sup>, 𝓓<sub>q-1</sub><sup>q</sup>) = {0}, if p ≠ q, 0 < p, q < ∞. If 0 < p, q < ∞, p ≠ q, 0 < s < 1 such that p + s, q + s > 1, then M(𝓓<sub>p-2+s</sub><sup>p</sup>, 𝓓<sub>q-2+s</sub><sup>q</sup>) = {0}. However, X ∩ 𝓓<sub>p-1</sub><sup>p</sup> ⊆ X ∩ 𝓓<sub>q-1</sub><sup>q</sup> and X ∩ 𝓓<sub>p-2+s</sub><sup>p</sup> ⊆ X ∩ 𝓓<sub>q-2+s</sub><sup>p</sup> whenever X is a subspace of the Bloch space 𝓑 and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ 𝓓 <sub>p-2+s</sub><sup>p</sup>, X∩𝓓<sub>q-2+s</sub><sup>q</sup>) is nontrivial. In this paper, we study the multipliers M(X ∩ 𝓓<sub>p-2+s</sub><sup>p</sup>, X ∩ 𝓓<sub>q-2+s</sub><sup>q</sup>) for distinct classical subspaces X of the Bloch space 𝓑, where X = 𝓑, BMOA or 𝓗<sup>∞</sup>.
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ON ABSOLUTE VALUES OF <sub>K</sub> FUNCTIONS
Bao, Guanlong,Lou, Zengjian,Qian, Ruishen,Wulan, Hasi Korean Mathematical Society 2016 대한수학회보 Vol.53 No.2
In this paper, the effect of absolute values on the behavior of functions f in the spaces $\mathcal{Q}_K$ is investigated. It is clear that $g{\in}\mathcal{Q}_K({\partial}{\mathbb{D}}){\Rightarrow}{\mid}g{\mid}{\in}\mathcal{Q}_K({\partial}{\mathbb{D}})$, but the converse is not always true. For f in the Hardy space $H^2$, we give a condition involving the modulus of the function only, such that the condition together with ${\mid}f{\mid}{\in}\mathcal{Q}_K({\partial}{\mathbb{D}})$ is equivalent to $f{\in}\mathcal{Q}_K$. As an application, a new criterion for inner-outer factorisation of $\mathcal{Q}_K$ spaces is given. These results are also new for $Q_p$ spaces.
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