• 대한수학회보
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• 제41권3호
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• pp.413-418
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• 2004

Invertible and isometric composition operators acting on vector-valued Hardy space $H^2$(E) are characterized.

• 대한수학회보
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• 제45권4호
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• pp.681-687
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• 2008

We give a characterization of trans-separability for the function spaces ($C_b(X,\;E)$, $\beta$), (C(X, E), k) and ($C_b(X,\;E)$, u) in the case of E any general topological vector space.

• 대한수학회지
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• 제37권5호
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• pp.849-856
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• 2000

We give a new saddle point theorem for vector-valued functions on an admissible compact convex set in a topological vector space under weak condition that is the semicontinuity of two function scalarization and acyclicty of the involved sets. As application, we obtain the minimax theorem.

• 대한수학회보
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• 제21권1호
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• pp.31-31
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• 1984

• 한국수학교육학회지시리즈A:수학교육
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• 제24권1호
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• pp.11-16
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• 1985

• 대한수학회지
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• 제45권6호
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• pp.1561-1576
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• 2008

In this paper we shall prove some weighted norm inequalities of the form $${\int}_{R^n}\;|Tf(x)|^pu(x)dx\;{\leq}\;C_p\;{\int}_{R^n}\;|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.

• 대한수학회지
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• 제60권1호
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• pp.33-69
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• 2023

Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝⁿ → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

• 대한수학회지
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• 제54권1호
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• pp.319-357
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• 2017

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.489-496
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• 2007

Let g be a continuous function on an interval I which is not constant on any subinterval of I, and let ${\mu}$ be a Borel measure on I. In this paper we give a necessary and sufficient conditions guaranteeing, for the strongly measurable function f on I with values in a Banach space X, the existence of a continuous primitive function F on I with respect to g.

• 대한수학회보
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• 제58권2호
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• pp.403-417
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• 2021

This note is devoted to establishing the boundedness for some classes of Littlewood-Paley square operators defined by the kernels without any regularity on the mixed radial-angular spaces. The corresponding vector-valued versions are also presented. As applications, the corresponding results for the Littlewood-Paley g∗λ function and the Littlewood-Paley function related to the area integrals are also obtained.