• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.465-483
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• 2021

Let 𝓗(𝔻) be the space of analytic functions on the unit disc 𝔻. Let 𝜓 = (𝜓_j)ⁿ_j=0 and 𝚽 = (𝚽_j)ⁿ_j=0 be such that 𝜓_j, 𝚽_j ∈ 𝓗(𝔻). The linear differential operator is defined by T_𝜓(f) = ∑ⁿ_j=0 𝜓_jf^(j), f ∈ 𝓗(𝔻). We characterize the boundedness and compactness of the difference operator (T_𝜓 - T_𝚽)(f) = ∑ⁿ_j=0 (𝜓_j - 𝚽_j) f^(j) between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (non compact) differential operators such that their difference is bounded (compact).

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1923-1936
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• 2013

We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley $g^*_{\lambda}$-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by BMO functions are also considered.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1535-1548
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• 2008

The analogues of Marcinkiewicz multiplier theorem and Littlewood-Paley theorem are proved for p-Faber series in weighted Smirnov spaces defined on bounded and unbounded components of a rectifiable Jordan curve.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.321-325
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• 2007

We prove the Medina's results about the existence and uniqueness of solutions of discrete Volterra equations of convolution type in weighted spaces, by using the well-known Contraction Mapping Principle.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.767-779
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• 2021

Schatten-Herz class Toeplitz operators on weighted Bergman spaces induced by doubling weights are investigated in this paper.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.623-636
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• 2023

In this paper, we prove some vanishing theorems under the assumptions of weighted BiRic curvature or m-Bakry-Émery-Ricci curvature bounded from below.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.455-462
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• 2011

An analytic self-map ${\phi}$ of the open unit disk $\mathbb{D}$ in the complex plane and an analytic map ${\psi}$ on $\mathbb{D}$ induce the so-called weighted composition operator $C_{{\phi},{\psi}}$: $H(\mathbb{D})\;{\rightarrow}\;H(\mathbb{D})$, $f{\mapsto} \;{\psi}\;(f\;o\;{\phi})$, where H($\mathbb{D}$) denotes the set of all analytic functions on $\mathbb{D}$. We study when such an operator acting between different weighted Bergman spaces is bounded, compact and Schatten class.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.823-833
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• 2000

In this paper, we develop the method of quasilinearization comvined with the methos of upper and lower solutions for singular second order boundary value problems in weighted spaces. The sequences constructed converge uniformly and monotonically to the unique of the second singular order boundary value problem. Further we prove the rate of convergence is quadratic.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.457-473
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• 2019

In this paper, we investigate weak laws of large numbers for weighted coordinatewise pairwise negative quadrant dependence random vectors in Hilbert spaces in the case that the decay order of tail probability is r for some 0 < r < 2. Moreover, we extend results concerning Pareto-Zipf distributions and St. Petersburg game.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.753-762
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• 2012

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane. We also prove new analogous results in the context of bounded strictly pseudoconvex domains with smooth boundary.