• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.789-805
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• 2005

In this paper we consider analogous of Gronwall-type inequalities involving iterated integrals in the inequality (1.2) for functions when the function u in the right-hand side of the in­equality (1.2) is replaced by the function $u^P$ for some p. These inequalities are effective tools in the study of a system of an integral equation. We also provide some integral inequalities involving iterated integrals.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.563-578
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• 2006

The main aim of the present paper is to establish some new Gronwall type inequalities involving iterated integrals and give some applications of the main results.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.331-353
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• 2008

Some new nonlinear retarded integral inequalities of Gronwall-like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No.3, pp. 563-578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated.

• Honam Mathematical Journal
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• v.12 no.1
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• pp.83-111
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• 1990

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.207-226
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• 2024

In this paper, the weighted L^p boundedness of multilinear commutators and multilinear iterated commutators generated by the multilinear singular integral operators with generalized kernels and BMO functions is established, where the weight is multiple weight. Our results are generalizations of the corresponding results for multilinear singular integral operators with standard kernels and Dini kernels under certain conditions.

• East Asian mathematical journal
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• v.31 no.5
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• pp.635-652
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• 2015

It is shown that for a general Haar shift operator, and a weight in the $A_2$ weight class, we establish the weighted norm estimate which linearly depends on $A_2$-characteristic $[w]_{A_2}$. Although the result is now well known, we introduce the new method, which is called the iterated Bellman function method, to provide the estimate.