• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1791-1809
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• 2018

Let T be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q(q{\in}(1,{\infty}))$ be the vector-valued operator defined by $T_qf(x)=({\sum}_{k=1}^{\infty}{\mid}T\;f_k(x){\mid}^q)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of L log L type for the grand maximal operator of T, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.

• East Asian mathematical journal
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• v.30 no.5
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• pp.609-616
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• 2014

In this paper we consider hyperbolic equations related to the p-Laplacian with a nonsmooth kernel. By exploiting a suitable implicit time-discretization technique we obtain the existence of global strong solution.

• East Asian mathematical journal
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• v.29 no.1
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• pp.69-82
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• 2013

In this paper we consider a doubly nonlinear Volterra equation related to the Leray-Lions with a nonsmooth kernel. By exploiting a suitable implicit time-discretization technique we obtain the existence of global strong solution.