• 제목/요약/키워드: Bloch space

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BOUNDED LINEAR FUNCTIONAL ON L1a(B) RELATED WITH $\mathcal{B}_q$q

  • Choi, Ki Seong
    • 충청수학회지
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    • 제14권2호
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    • pp.37-46
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    • 2001
  • In this paper, weighted Bloch spaces $\mathcal{B}_q$ are considered on the open unit ball in $\mathbb{C}^n$. In this paper, we will show that every Bloch function in $B_q$ induces a bounded linear functional on $L^1_a(\mathcal{B})$.

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BOUNDEDNESS OF 𝓒b,c OPERATORS ON BLOCH SPACES

  • Nath, Pankaj Kumar;Naik, Sunanda
    • Korean Journal of Mathematics
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    • 제30권3호
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    • pp.467-474
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    • 2022
  • In this article, we consider the integral operator 𝓒b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ where * denotes the Hadamard/ convolution product of power series, F(a, b; c; z) is the classical hypergeometric function with b, c > 0, b + 1 > c and f(0) = 0. We investigate the boundedness of the 𝓒b,c operators on Bloch spaces.

SOME APPLICATIONS FOR GENERALIZED FRACTIONAL OPERATORS IN ANALYTIC FUNCTIONS SPACES

  • Kilicman, Adem;Abdulnaby, Zainab E.
    • Korean Journal of Mathematics
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    • 제27권3호
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    • pp.581-594
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    • 2019
  • In this study a new generalization for operators of two parameters type of fractional in the unit disk is proposed. The fractional operators in this generalization are in the Srivastava-Owa sense. Concerning with the related applications, the generalized Gauss hypergeometric function is introduced. Further, some boundedness properties on Bloch space are also discussed.

ON HYPERHOLOMORPHIC Fαω,G(p, q, s) SPACES OF QUATERNION VALUED FUNCTIONS

  • Kamal, Alaa;Yassen, Taha Ibrahim
    • Korean Journal of Mathematics
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    • 제26권1호
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    • pp.87-101
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    • 2018
  • The purpose of this paper is to define a new class of hyperholomorphic functions spaces, which will be called $F^{\alpha}_{{\omega},G}$(p, q, s) type spaces. For this class, we characterize hyperholomorphic weighted ${\alpha}$-Bloch functions by functions belonging to $F^{\alpha}_{{\omega},G}$(p, q, s) spaces under some mild conditions. Moreover, we give some essential properties for the extended weighted little ${\alpha}$-Bloch spaces. Also, we give the characterization for the hyperholomorphic weighted Bloch space by the integral norms of $F^{\alpha}_{{\omega},G}$(p, q, s) spaces of hyperholomorphic functions. Finally, we will give the relation between the hyperholomorphic ${\mathcal{B}}^{\alpha}_{{\omega},0}$ type spaces and the hyperholomorphic valued-functions space $F^{\alpha}_{{\omega},G}$(p, q, s).

ON DUALITY OF WEIGHTED BLOCH SPACES IN ℂn

  • Yang, Gye Tak;Choi, Ki Seong
    • 충청수학회지
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    • 제23권3호
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    • pp.523-534
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    • 2010
  • In this paper, we consider the weighted Bloch spaces ${\mathcal{B}}_q$(q > 0) on the open unit ball in ${\mathbb{C}}^n$. We prove a certain integral representation theorem that is used to determine the degree of growth of the functions in the space ${\mathcal{B}}_q$ for q > 0. This means that for each q > 0, the Banach dual of $L_a^1$ is ${\mathcal{B}}_q$ and the Banach dual of ${\mathcal{B}}_{q,0}$ is $L_a^1$ for each $q{\geq}1$.

THE GROWTH OF BLOCH FUNCTIONS IN SOME SPACES

  • Wenwan Yang;Junming Zhugeliu
    • 대한수학회보
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    • 제61권4호
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    • pp.959-968
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    • 2024
  • Suppose f belongs to the Bloch space with f(0) = 0. For 0 < r < 1 and 0 < p < ∞, we show that $$M_p(r,\,f)\,=\,({\frac{1}{2\pi}}{\int_{0}^{2\pi}}\,{\mid}f(re^{it}){\mid}^pdt)^{1/p}\,{\leq}\,({\frac{{\Gamma}(\frac{p}{2}+1)}{{\Gamma}(\frac{p}{2}+1-k)}})^{1/p}\,{\rho}{\mathcal{B}}(log\frac{1}{1-r^2})^{1/2},$$ where ρʙ(f) = supz∈ⅅ(1 - |z|2)|f'(z)| and k is the integer satisfying 0 < p - 2k ≤ 2. Moreover, we prove that for 0 < r < 1 and p > 1, $${\parallel}f_r{\parallel}_{B_q}\,{\leq}\,r\,{\rho}{\mathcal{B}}(f)(\frac{1}{(1-r^2)(q-1)})^{1/q},$$ where fr(z) = f(rz) and ||·||ʙq is the Besov seminorm given by ║f║ʙq = (∫𝔻 |f'(z)|q(1-|z|2)q-2dA(z)). These results improve previous results of Clunie and MacGregor.

ON BOUNDED OPERATOR Qq IN WEIGHT BLOCH SPACE

  • Choi, Ki Seong
    • 충청수학회지
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    • 제13권1호
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    • pp.131-138
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    • 2000
  • Let D be the open unit disk in the complex plane $\mathbb{C}$. For any q > 0, the operator $Q_q$ defined by $$Q_qf(z)=q\int_{D}\frac{f(\omega)}{(1-z{\bar{\omega}})^{1+q}}d{\omega},\;z{\in}D$$. maps $L^{\infty}(D)$ boundedly onto $B_q$ for each q > 0. In this paper, weighted Bloch spaces $\mathcal{B}_q$ (q > 0) are considered on the open unit ball in $\mathbb{C}^n$. In particular, we will investigate the possibility of extension of this operator to the Weighted Bloch spaces $\mathcal{B}_q$ in $\mathbb{C}^n$.

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Lp-boundedness (1 ≤ p ≤ ∞) for Bergman Projection on a Class of Convex Domains of Infinite Type in ℂ2

  • Ly Kim Ha
    • Kyungpook Mathematical Journal
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    • 제63권3호
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    • pp.413-424
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    • 2023
  • The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ ℂ2, for 1 < p < ∞, the Bergman projection 𝓟 is bounded from Lp(Ω, dV ) to the Bergman space Ap(Ω); from L(Ω) to the holomorphic Bloch space BlHol(Ω); and from L1(Ω, P(z, z)dV) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.

ON DISTANCE ESTIMATES AND ATOMIC DECOMPOSITIONS IN SPACES OF ANALYTIC FUNCTIONS ON STRICTLY PSEUDOCONVEX DOMAINS

  • Arsenovic, Milos;Shamoyan, Romi F.
    • 대한수학회보
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    • 제52권1호
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    • pp.85-103
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    • 2015
  • We prove some sharp extremal distance results for functions in various spaces of analytic functions on bounded strictly pseudoconvex domains with smooth boundary. Also, we obtain atomic decompositions in multifunctional Bloch and weighted Bergman spaces of analytic functions on strictly pseudoconvex domains with smooth boundary, which extend known results in the classical case of a single function.

A NOTE OF WEIGHTED COMPOSITION OPERATORS ON BLOCH-TYPE SPACES

  • LI, SONGXIAO;ZHOU, JIZHEN
    • 대한수학회보
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    • 제52권5호
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    • pp.1711-1719
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    • 2015
  • We obtain a new criterion for the boundedness and compactness of the weighted composition operators ${\psi}C_{\varphi}$ from ${\ss}^{{\alpha}}$(0 < ${\alpha}$ < 1) to ${\ss}^{{\beta}}$ in terms of the sequence $\{{\psi}{\varphi}^n\}$. An estimate for the essential norm of ${\psi}C_{\varphi}$ is also given.