• East Asian mathematical journal
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• v.31 no.5
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• pp.667-675
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• 2015

In this paper, we provide some properties of several left regular functions in Clifford analysis. We find the corresponding Cauchy-Riemann system and conjugate harmonic functions of the harmonic functions, for each left regular function in the sense of several complex variables. And we investigate certain properties of generalized quaternions in Clifford analysis.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.1-3
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• 2002

In this paper, we obtain some coefficient bounds of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.377-381
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• 2005

We present a convenient recursive formula for the sums of alternating harmonic series of odd order. The recursion is obtained by expanding in Fourier series certain elementary functions.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.507-516
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• 2007

Let M be a complete Riemannian manifold and L be a $Schr\"{o}dinger$ operator on M. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded L-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on the L-nonparabolic end, which vanish at the boundary of the end.

• 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}$.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.481-484
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• 2003

We will show that if U is a Bergman ball E($\alpha;\;\delta$) in $B_n\;\subset\;{\mathbb{C}_n}$ and if U has M-harmonic volume mean value property at a for all M-harmonic functions f on $\={U} $, then U must be a ball centered at the origin with $\alpha\;=\;0$.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.269-278
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• 2021

In this paper, we investigate harmonic univalent functions convex in the direction 𝜃, for 𝜃 ∈ [0, 𝜋). We find bounds for |f_z(z)|, ${\mid}f_{\bar{z}}(z){\mid}$ and |f(z)|, as well as coefficient bounds on the series expansion of functions convex in a given direction.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.959-971
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• 1997

In the paper we introduce Hausdorff measures which are suitable or the study of Lipschitz regularity of M-harmonic function in the unit ball B in $C^n$. For an M-harmonic function h which satisfies certain integrability conditions, we show that there is an open set $\Omega$, whose Hausdorff content is arbitrarily small, such that h is Lipschitz smooth on $B \backslash \Omega$.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.1003-1016
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• 2016

In this paper, we introduce a new kind of slant helix for null curves called null $W_n$-slant helix and we give a definition of new harmonic curvature functions of a null curve in terms of $W_n$ in (n + 2)-dimensional Lorentzian space $M^{n+2}_1$ (for n > 3). Also, we obtain a characterization such as: "The curve ${\alpha}$ s a null $W_n$-slant helix ${\Leftrightarrow}H^{\prime}_n-k_1H_{n-1}-k_2H_{n-3}=0$" where $H_n,H_{n-1}$ and $H_{n-3}$ are harmonic curvature functions and $k_1,k_2$ are the Cartan curvature functions of the null curve ${\alpha}$.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.137-159
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• 2013

It is studied the linear combinations of composition operators on the Banach space of bounded harmonic functions on the open unit disk. We determine the essential norm of them.