• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.405-417
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• 2008

In this paper we prove some Hardy inequalities in the half space of the Heisenberg group and indicate the sharp constant.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.411-423
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• 2007

This paper deals with a reverse Hardy-Hilbert's inequality with a best constant factor by introducing two parameters ${\lambda}$ and ${\alpha}$. We also consider the equivalent form and the analogue integral inequalities. Some particular results are given.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1135-1143
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• 2019

The matrix representation of the Toeplitz operator on the Hardy space with respect to a generalized orthonormal basis for the space of square integrable functions associated to a bounded simply connected region in the complex plane is completely computed in terms of only the Szegő kernel and the Garabedian kernels.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.691-700
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• 2021

In this paper, we compute directly the Hankel matrix representation of the Hankel operator on the Hardy space of the unit disc without using any classical kernel functions with respect to special orthonormal bases for the Hardy space and its orthogonal complement. This gives an elementary proof for the formula.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.315-346
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• 2023

We present a variety of univariate and multivariate left and right side Hardy type fractional inequalities, many of them under convexity, and other also of L_p type, p ≥ 1, in the setting of generalized Hilfer and Prabhakar fractional Calculi.

• Journal of English Language & Literature
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• v.64 no.4
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• pp.551-564
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• 2018

Laodiceanism is the blueprint from which Hardy draws one of his most ingenuous effects: the creating of a Laodicean around which the novel constructs its ambiguity. Hardy's command of "ingenuity" joins both the leading heroine Paula and the minor character Dare into the same category of a Laodicean. Alongside Paula, Dare is the most important ingredient in the novel in that he acts as an enigmatic persona defying the reader's attempts to establish a coherent type. This paper aims to offer a close reading of Dare's life story, which is chosen for discussion as he has been deemed as a simple functionary and thus apparently escaped serious critical notice thus far. It is stressed that the structure of sensations Dare embodies is fascinating in the sense that it is a locus where the coexistence of both meaning and nonmeaning would not amount to harmonious peace or stability so much as permits the impossibility of single and central significance. In this coexistence is inscribed a notion that the binaries in opposition are endlessly inter-mingled in dialogic tension, which is the hallmark of Laodiceanism that Hardy aims to present through the creation of Dare.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• English Language & Literature Teaching
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• v.11 no.2
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• pp.171-194
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• 2005

The essay attempts at a critical reading of Thomas Hardy's The Mayor of Casterbridge (1886) in terms of character and socio-cultural change. Juxtaposing the story of Michael Henchard's career with the social and economic changes in the agricultural town, it attempts to elaborate on the complex ways in which Hardy relates the old modes of life and thinking to the material culture. Though the novel is centered on the story of Henchard, the Henchard-Farfrae clash represents the conflict of "old" and "new" modes of socio-economic organization and consciousness. The story of the rustic man of character struggling with his contradictory traits of strong will-power and emotional collapse suggests that Hardy's literary representation of the rural community and the rustic protagonist is deeply rooted in historical reality. However, while there is the interlocking of the changes in personal fate and social change, the representation is a "reinvented" literary construction with complex mediation. Despite the narrator's emphasis on Henchard's immutability, peculiarity, and resilience, his character is, in a complex, mediated way, shaped by the material conditions of English rural community in the late 19th century. The mediating role of Elizabeth-Jane as a narrative resolution embodies Hardy's ambivalent historical position concerning the period undergoing change and conflict.

• Microbiology and Biotechnology Letters
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• v.41 no.3
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• pp.327-334
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• 2013

For the development of hardy kiwi wine, we arranged for the post-maturity of hardy kiwi fruit, treated them with calcium carbonate and a pectinase enzyme complex, investigated the resulting physicochemical properties and conducted a sensory evaluation. The period determined for creating post-maturity in the hardy kiwi fruit was determined as 5 days storage at room temperature following maturity. During this time the yield of fruit juice was increased from 22.1% to 53.5% using 0.1% (v/v) cytolase PCL5 for 2 h at room temperature. 0.1% (w/v) calcium carbonate was also added during the process of aging, for the reduction of the sour taste. The fermentation trial of the hardy kiwi wine was prepared using water (25% or 50%), sugar ($24^{\circ}brix$), 0.1% (w/v) $CaCO_3$, 0.1% (v/v) cytolase PCL5, $K_2S_2O_5$ (200 ppm), and yeast ($1.5{\times}10^7$ cell/ml). Fermentation then occurred for 2 weeks at $20^{\circ}C$. The pH value, total acidity, alcohol, and reducing sugar content of the resulting hardy kiwi wines of 25% (v/w) and 50% (v/w) water, were in a range of pH 3.4-3.7, 1.12-1.21%, 14.3-14.4%, and 15-16 g/l, respectively. Citric acid and fructose constituted the major organic acids and the free sugar of the 25% and 50% hardy kiwi wine, respectively. Volatile flavor components, including 10 kinds of esters, 8 kinds of alcohols, 5 kinds of acids, 3 kinds of others and aldehydes, were determined by GC analysis. The results of sensory evaluation demonstrated that 50% hardy kiwi wine is more palatable than 25% hardy kiwi wine.