• 대한수학회보
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• 제18권1호
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• pp.17-19
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• 1981

• 대한수학회지
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• 제41권1호
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• pp.95-105
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• 2004

In this paper we will consider the weighted composition operators W = $uC_{\tau}$ between $L^{p}$$(X,\sum,\mu$) spaces and Orlicz spaces $L^{\phi}$$(X,\sum,\mu$) generated by measurable and non-singular transformations $\tau$ from X into itself and measurable functions u on X. We characterize the functions u and transformations $\tau$ that induce weighted composition operators between $L^{p}$ -spaces by using some properties of conditional expectation operator, pair (u,${\gamma}$) and the measure space $(X,\sum,\mu$). Also, some other properties of these types of operators will be investigated.

• 대한수학회논문집
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• 제36권3호
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• pp.447-463
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• 2021

In this paper we study the existence and long-time behavior of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators with a new class of nonlinearities. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence of global attractors by using the asymptotic a priori estimates method.

• 충청수학회지
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• 제30권2호
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• pp.227-238
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• 2017

The existence of solutions for nonlinear elliptic partial differential equations with general flux and damping terms is investigated.

• 대한수학회보
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• 제36권2호
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• pp.225-231
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• 1999

Let Mf(x) be the Hardy-Littlewood maximal function on $\mathbb{R}^n$. Let $\Phi$ and $\Psi$ be functions satisfying $\Phi$(t) = ${\int^t}_0$a(s)ds and $\Psi(t)$ = ${\int^t}_0$b(s)ds, where a(s) and b(s) are positive continuous such that ${\int^\infty}_0\frac{a(s)}{s}ds$ = $\infty$ and b(s) is quasi-increasing. We show that if there exists a constant $c_1$ so that ${\int^s}_0\frac{a(t)}{t}dt\;c_1b(c_1s)$ for all $s\geq0$, then there exists a constant $c_1$ such that(0.1) $\int_{\mathbb{R^{n}}$ $\Phi(Mf(x))dx\;\leq\;c_2$ $\int_\mathbb{R^{n}}$$\Psi(c_2\midf(x)\mid)dx$ for all $f\epsilonL^1(R^n_$. Conversely, if there exists a constant $c_2$ satisfying the condition (0.1), then there exists a constant $c_1$ so that ${\int^s}_\delta\frac{a(t)}{t}dt=;\leq\;c_1b(c_1s$ for all $\delta$ > 0 and $s\geq\delta$.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.11-22
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• 2014

The sequence spaces $c^F$(M), $c^F_0$(M) and ${\ell}^F$(M) of fuzzy real numbers with fuzzy metric are introduced. Some properties of these sequence spaces like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving these sequence spaces.

• 대한수학회지
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• 제51권6호
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• 충청수학회지
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• 제31권1호
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• pp.43-46
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• 2018

It is concerned with the continuity of the Hardy-Little wood maximal function between the classical Lebesgue spaces or the Orlicz spaces. A new approach to the continuity of the Hardy-Littlewood maximal function is presented through the observation that the continuity is closely related to the existence of solutions for a certain type of first order ordinary differential equations. It is applied to verify the continuity of the Hardy-Littlewood maximal function from $L^p({\mathbb{R}}^n)$ to $L^q({\mathbb{R}}^n)$ for 1 ${\leq}$ q < p < ${\infty}$.

• 호남수학학술지
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• 제43권2호
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• pp.343-357
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• 2021

In the present paper, we introduce the concepts of $\mathcal{I}$-asymptotically statistical $\tilde{\phi}$-equivalence and $\mathcal{I}$-asymptotically lacunary statistical $\tilde{\phi}$-equivalence for triple sequences. Moreover, we give the relations between these new notions.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.433-444
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• 2022

In the present paper, we introduce some new notions of Wijsman ${\mathcal{I}}$-statistical convergence with the use of Orlicz function, lacunary sequence and triple sequences of sets, and obtain some analogous results from the new definitions point of views.