• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.425-435
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• 2023

The classical Hardy Theorem on R states that a function f and its Fourier transform cannot be simultaneously very small; this fact was generalized by Miyachi in terms of L¹ + L^∞ and log⁺-functions. In this paper, we consider the k-Hankel transform, which is a deformation of the Hankel transform by a parameter k > 0 arising from Dunkl's theory. We study Miyachi's theorem for the k-Hankel transform on ℝ^d.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1229-1236
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• 2009

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator S$_K$ on a vector-valued Hardy space H$^2$(${\Omega}$, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions and quasi-inner divisors.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.89-96
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• 2004

We prove de Leeuw's restriction theorem result Jodeit, Jr. [4] for multipliers on $H^{p}$ spaces, p＜1.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.257-262
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• 2014

In this note we consider "generalized Riesz points" for compact and quasinilpotent perturbations of Toeplitz operators acting on the Hardy space of the unit circle.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.1057-1072
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• 2023

Let 𝜑 : ℝⁿ × [0, ∞) → [0, ∞) be a growth function and H^𝜑(ℝⁿ) the Musielak-Orlicz Hardy space defined via the non-tangential grand maximal function. A general summability method, the so-called 𝜃-summability is considered for multi-dimensional Fourier transforms in H^𝜑(ℝⁿ). Precisely, with some assumptions on 𝜃, the authors first prove that the maximal operator of the 𝜃-means is bounded from H^𝜑(ℝⁿ) to L^𝜑(ℝⁿ). As consequences, some norm and almost everywhere convergence results of the 𝜃-means, which generalizes the well-known Lebesgue's theorem, are then obtained. Finally, the corresponding conclusions of some specific summability methods, such as Bochner-Riesz, Weierstrass and Picard-Bessel summations, are also presented.

• East Asian mathematical journal
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• v.6 no.2
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• pp.133-144
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• 1990

In 1982, N. Miller [5] showed a weighted $L^p$ boundedness theorem for pseudo differential operators with symbols $S^0_{1.0}$. In this paper, we shall prove the pointwise estimates, in terms of the Fefferman, Stein sharp function and Hardy Littlewood maximal function, for pseudo differential operators with reduced symbols and show a weighted $L^p$-boundedness for pseudo differential operators with symbol in $S^m_{\rho,\delta}$, 0{$\leq}{\delta}{\leq}{\rho}{\leq}1$, ${\delta}{\neq}1$, ${\rho}{\neq}0$ and $m=(n+1)(\rho-1)$.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.385-394
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• 1997

In this paper, we prove in p-uniforlmy convex space a fixed point theorem for a class of mappings T satsfying: for each x, y in the domain and for n = 1, 2, 3, $\cdots$, $$ \left\$\mid$ T^n x - T^n y \right\$\mid$ \leq a \cdot \left\$\mid$ x - y \right\$\mid$ + b(\left\$\mid$ x - T^n x \right\$\mid$ + \left\$\mid$ y - T^n y \right\$\mid$) + c(\left\$\mid$ c - T^n y \right\$\mid$ + \left\$\mid$ y - T^n x \right\$\mid$, $$ where a, b, c are nonnegative constants satisfying certain conditions. Further we establish some fixed point theorems for these mappings in a Hilbert space, in $L^p$ spaces, in Hardy spaces $H^p$ and in Sobolev spaces $H^{p,k}$ for 1 < p < $\infty$ and k $\leq$ 0. As a consequence of our main result, we also the results of Goebel and Kirk [7], Lim [8], Lifshitz [12], Xu [20] and others.

• Asian-Australasian Journal of Animal Sciences
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• v.29 no.1
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• pp.36-42
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• 2016

Milk-related traits (milk yield, fat and protein) have been crucial to selection of Holstein. It is essential to find the current selection trends of Holstein. Despite this, uncovering the current trends of selection have been ignored in previous studies. We suggest a new formula to detect the current selection trends based on single nucleotide polymorphisms (SNP). This suggestion is based on the best linear unbiased prediction (BLUP) and the Fisher's fundamental theorem of natural selection both of which are trait-dependent. Fisher's theorem links the additive genetic variance to the selection coefficient. For Holstein milk production traits, we estimated the additive genetic variance using SNP effect from BLUP and selection coefficients based on genetic variance to search highly selective SNPs. Through these processes, we identified significantly selective SNPs. The number of genes containing highly selective SNPs with p-value <0.01 (nearly top 1% SNPs) in all traits and p-value <0.001 (nearly top 0.1%) in any traits was 14. They are phosphodiesterase 4B (PDE4B), serine/threonine kinase 40 (STK40), collagen, type XI, alpha 1 (COL11A1), ephrin-A1 (EFNA1), netrin 4 (NTN4), neuron specific gene family member 1 (NSG1), estrogen receptor 1 (ESR1), neurexin 3 (NRXN3), spectrin, beta, non-erythrocytic 1 (SPTBN1), ADP-ribosylation factor interacting protein 1 (ARFIP1), mutL homolog 1 (MLH1), transmembrane channel-like 7 (TMC7), carboxypeptidase X, member 2 (CPXM2) and ADAM metallopeptidase domain 12 (ADAM12). These genes may be important for future artificial selection trends. Also, we found that the SNP effect predicted from BLUP was the key factor to determine the expected current selection coefficient of SNP. Under Hardy-Weinberg equilibrium of SNP markers in current generation, the selection coefficient is equivalent to $2^*SNP$ effect.