• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.553-564
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• 2007

In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(<{\theta}_1,\;y>),\ldots,<{\theta}_n,\;y>)$ for s-a.e. $y{\in}C_0[0,\;T]$, where $<{\theta},\;y>$ denotes the Riemann-Stieltjes integral ${\int}_0^T{\theta}(t)\;dy(t)$.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.97-119
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• 2008

Electrical impedance tomography (EIT) problem with anisotropic anomalous region is formulated in a few different ways using boundary integral operators. The Frechet derivative of Neumann-to-Dirichlet map is computed also by using boundary integral operators and the boundary of the anomalous region is approximated by trigonometric expansion with Lagrangian basis. The numerical reconstruction is done in case that the conductivity of the anomalous region is isotropic.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.297-306
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• 2010

In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree - $\lambda$ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.

• East Asian mathematical journal
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• v.29 no.5
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• pp.545-550
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• 2013

A remarkably large number of integral formulas have been investigated and developed. Certain large number of integral formulas are expressed as derivatives of some known functions. Here we choose to recall such a formula to present explicit expressions in terms of Gamma function, Psi function and Polygamma functions. Some simple interesting special cases of our main formulas are also considered. It is also pointed out that the same argument can establish explicit integral formulas for other those expressed in terms of derivatives of some known functions.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.231-236
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• 2006

In this paper, we study the Henstock-Pettis integral of Banach space-valued functions mapping an interval [0, 1] in R into a Banach space X. In particular, we show that a Henstock integrable function on [0, 1] is Henstock-Pettis integrable on [0, 1] and a Pettis integrable function is Henstock-Pettis integrable on [0, 1].

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.141-148
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• 2012

In this paper we define the AP-$GR_{k}$ integral and investigate some properties of this integral. Also, a convergence theorem is proved using equi-integrability conditions.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.31-48
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• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.71-84
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• 2007

In this paper, we define the C-Stieltjes integral of the functions mapping an interval [a,b] into a Banach space X with respect to g on [a,b], and the C-Stieltjes representable operators for the vector-valued functions which are the generalizations of the Henstock-Stieltjes representable operators. Some properties of the C-Stieltjes operators and the convergence theorems of the C-Stieltjes integral are given.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.811-815
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• 1998

In this paper we define a sample path-valued conditional Yeh-Wiener integral for function F of the type E[F(x)$\mid$x(*,(equation omitted))=$\psi({\blacktriangle})]$, where $\psi$ is in C[0, (equation omitted)] and ${\blacktriangle}$ = (equation omitted) and evaluate a sample path-valued conditional Yeh-Wiener integral using the result obtained.

• 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.