• Title/Summary/Keyword: Harmonic Bergman Functions

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BERGMAN SPACES, BLOCH SPACES AND INTEGRAL MEANS OF p-HARMONIC FUNCTIONS

  • Fu, Xi;Qiao, Jinjing
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.2
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    • pp.481-495
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    • 2021
  • In this paper, we investigate the properties of Bergman spaces, Bloch spaces and integral means of p-harmonic functions on the unit ball in ℝn. Firstly, we offer some Lipschitz-type and double integral characterizations for Bergman space ��kγ. Secondly, we characterize Bloch space ��αω in terms of weighted Lipschitz conditions and BMO functions. Finally, a Hardy-Littlewood type theorem for integral means of p-harmonic functions is established.

WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

  • Koo, HYUNGWOON;NAM, KYESOOK;YI, HEUNGSU
    • Journal of the Korean Mathematical Society
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    • v.42 no.5
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    • pp.975-1002
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    • 2005
  • On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\infty$ and nonorthogonal projections for 1 $\leq$ p < $\infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.

TOEPLITZ OPERATORS ON HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

  • Yi, HeungSu
    • Korean Journal of Mathematics
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    • v.7 no.2
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    • pp.271-280
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    • 1999
  • We study Toeplitz operators on the harmonic Bergman Space $b^p(\mathbf{H})$, where $\mathbf{H}$ is the upper half space in $\mathbf{R}(n{\geq}2)$, for 1 < $p$ < ${\infty}$. We give characterizations for the Toeplitz operators with positive symbols to be bounded.

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HARMONIC CONJUGATES OF WEIGHTED HARMONIC BERGMAN FUNCTIONS ON HALF-SPACES

  • Nam, Kye-Sook;Yi, Heung-Su
    • Communications of the Korean Mathematical Society
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    • v.18 no.3
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    • pp.449-457
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    • 2003
  • On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.

Poisson integrals contained in harmonic bergman spaces on upper half-space

  • Yi, Heung-Su
    • Communications of the Korean Mathematical Society
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    • v.12 no.1
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    • pp.51-58
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    • 1997
  • On the setting of the upper half-space, H of the euclidean n-space, we consider the question of when the Poisson integral of a function on the boundary of H is a harmonic Bergman function and here we give a partial answer.

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THE ATOMIC DECOMPOSITION OF HARMONIC BERGMAN FUNCTIONS, DUALITIES AND TOEPLITZ OPERATORS

  • Lee, Young-Joo
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.263-279
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    • 2009
  • On the setting of the unit ball of ${\mathbb{R}}^n$, we consider a Banach space of harmonic functions motivated by the atomic decomposition in the sense of Coifman and Rochberg [5]. First we identify its dual (resp. predual) space with certain harmonic function space of (resp. vanishing) logarithmic growth. Then we describe these spaces in terms of boundedness and compactness of certain Toeplitz operators.

CONFORMAL MAPPING AND CLASSICAL KERNEL FUNCTIONS

  • CHUNG, YOUNG-BOK
    • Honam Mathematical Journal
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    • v.27 no.2
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    • pp.195-203
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    • 2005
  • We show that the exact Bergman kernel function associated to a $C^{\infty}$ bounded domain in the plane relates the derivatives of the Ahlfors map in an explicit way. And we find several formulas relating the exact Bergman kernel to classical kernel functions in potential theory.

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