• 대한수학회지
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• 제58권4호
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• pp.1035-1058
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• 2021

Under certain rather weak size conditions assumed on the kernels, some weighted norm inequalities for singular integral operators, related maximal operators, maximal truncated singular integral operators and Marcinkiewicz integral operators in nonisotropic setting will be shown. These weighted norm inequalities will enable us to obtain some vector valued inequalities for the above operators.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권2호
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• pp.39-53
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• 2021

In this paper, we investigate several new weighted fractional integral inequalities by considering Marichev-Saigo-Maeda (MSM) fractional integral operator.

• Korean Journal of Mathematics
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• 제18권1호
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• pp.63-77
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• 2010

Infinite finite range inequalities relate the norm of a weighted polynomial over ${\mathbb{R}}$ to its norm over a finite interval. In this paper we extend such inequalities to generalized polynomials with the weight $W(x)={\prod}^{m}_{k=1}{\mid}x-x_k{\mid}^{{\gamma}_k}{\cdot}{\exp}(-{\mid}x{\mid}^{\alpha})$.

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.155-171
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• 2018

Some weighted integral inequalities of Hermite-Hadamard type for GG-convex functions defined on positive intervals are given. Applications for special means are also provided.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.12-12
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• 2000

This paper consider a new weighted model reduction using block diagonal solutions of Lyapunov inequalities. With the input and/or output weighting function, the stability of reduced order system is quaranteed and a priori error bound is proposed. to achieve this, after finding the solutions of two Lyapunov inequalities and balancing the full order system, we find the reduced order systems using the direct truncation and the singular perturbation approximation. The proposed method is compared with other existing methods using numerical example.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.717-737
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• 2020

In this paper, we establish some weighted generalization of Opial type inequalities in two independent variables for two functions. We also obtain weighted Opial type inequalities by using p-norms. Special cases of our results reduce to the inequalities in earlier study.

• 대한수학회보
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• 제45권3호
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• pp.477-483
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• 2008

In this paper, by introducing parameter r>1, new weighted Ostrowski-Gruss-Cebysev type inequalities for 1/p+11/q=1-1/r are established.

• 대한수학회보
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• 제60권2호
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• pp.325-338
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• 2023

In this paper, we derive a Reilly-type inequality for the Laplacian with density on weighted manifolds with boundary. As its applications, we obtain some new Poincaré-type inequalities not only on weighted manifolds, but more interestingly, also on their boundary. Furthermore, some mean-curvature type inequalities on the boundary are also given.

• 대한수학회지
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• 제44권6호
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• pp.1233-1241
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• 2007

We derive a kind of weighted norm inequalities which relate the commutators of potential type operators to the corresponding maximal operators.

• 대한수학회지
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• 제58권1호
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• pp.69-90
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• 2021

In this paper, we prove weighted norm inequalities for rough singular integrals along surfaces with radial kernels h and sphere kernels Ω by assuming h ∈ △γ(ℝ+) and Ω ∈ ����β(Sn-1) for some γ > 1 and β > 1. Here Ω ∈ ����β(Sn-1) denotes the variant of Grafakos-Stefanov type size conditions on the unit sphere. Our results essentially improve and extend the previous weighted results for the rough singular integrals and the corresponding maximal truncated operators.