• Title/Summary/Keyword: LOG operator

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REMARKS ON SPECTRAL PROPERTIES OF p-HYPONORMAL AND LOG-HYPONORMAL OPERATORS

  • DUGGAL BHAGWATI P.;JEON, IN-HO
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.543-554
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    • 2005
  • In this paper it is proved that for p-hyponormal or log-hyponormal operator A there exist an associated hyponormal operator T, a quasi-affinity X and an injection operator Y such that TX = XA and AY = YT. The operator A and T have the same spectral picture. We apply these results to give brief proofs of some well known spectral properties of p-hyponormal and log­hyponormal operators, amongst them that the spectrum is a con­tinuous function on these classes of operators.

CERTAIN MAXIMAL OPERATOR AND ITS WEAK TYPE $L^1$($R^n$)-ESTIMATE

  • Kim, Yong-Cheol
    • Communications of the Korean Mathematical Society
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    • v.16 no.4
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    • pp.621-626
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    • 2001
  • Let { $A_{>o}$ t= exp(M log t)} $_{t}$ be a dilation group where M is a real n$\times$n matrix whose eigenvalues has strictly positive real part, and let $\rho$be an $A_{t}$ -homogeneous distance function defined on ( $R^{n}$ ). Suppose that K is a function defined on ( $R^{n}$ ) such that /K(x)/$\leq$ (No Abstract.see full/text) for a decreasing function defined on (t) on R+ satisfying where wo(x)=│log│log (x)ll. For f$\in$ $L_{1}$ ( $R^{n}$ ), define f(x)=sup t>0 Kt*f(x)=t-v K(Al/tx) and v is the trace of M. Then we show that \ulcorner is a bounded operator of $L_{-{1}( $R^{n}$ ) into $L^1$,$\infty$( $R^{n}$).

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QUANTITATIVE WEIGHTED BOUNDS FOR THE VECTOR-VALUED SINGULAR INTEGRAL OPERATORS WITH NONSMOOTH KERNELS

  • Hu, Guoen
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1791-1809
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    • 2018
  • Let T be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q(q{\in}(1,{\infty}))$ be the vector-valued operator defined by $T_qf(x)=({\sum}_{k=1}^{\infty}{\mid}T\;f_k(x){\mid}^q)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of L log L type for the grand maximal operator of T, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.

ON JOINT WEYL AND BROWDER SPECTRA

  • Kim, Jin-Chun
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.53-62
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    • 2000
  • In this paper we explore relations between joint Weyl and Browder spectra. Also, we give a spectral characterization of the Taylor-Browder spectrum for special classes of doubly commuting n-tuples of operators and then give a partial answer to Duggal's question.

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LIPSCHITZ CONTINUOUS AND COMPACT COMPOSITION OPERATOR ACTING BETWEEN SOME WEIGHTED GENERAL HYPERBOLIC-TYPE CLASSES

  • Kamal, A.;El-Sayed Ahmed, A.;Yassen, T.I.
    • Korean Journal of Mathematics
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    • v.24 no.4
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    • pp.647-662
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    • 2016
  • In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.

Investigation of Microbial Contamination of Dutch Coffee Sold at Food Service Business Operator (식품접객업소에서 판매되는 더치커피의 미생물 오염도 조사)

  • Lee, Hyo-Kyung;Do, Young-Sook;Park, Geon-Yeong;Lee, Hyun-Kyung;Choi, Yu-Mi;Lim, Hye-Won;Ham, Hyun-Kyung;Han, Yu-Ri;Lee, Myung-Jin
    • Journal of Food Hygiene and Safety
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    • v.37 no.4
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    • pp.271-276
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    • 2022
  • This study aimed to investigate microbial contamination of Dutch coffee in Gyeonggi province, South Korea. A total of 70 different Dutch coffee were purchased from an offline market (food service business operator). Two types of coffee were considered: "coffee made from food service business operator" and "coffee made from food manufacturer." The levels of total aerobic bacteria were 0.74-6.21 log CFU/mL in 15 samples and fungi were 0.70-4.00 log CFU/mL in 21 samples. Total aerobic bacteria was detected at higher levels in "coffee made from food service business operator" than in "coffee made from food manufacturer," and the difference was not significant. Three samples in "coffee made from food manufacturer" exceeded the standard for total aerobic bacteria. Escherichia coli, Coliform, and 12 types of foodborne bacteria were not detected in all samples. The extraction method detected no difference in cell counts of total aerobic bacteria and fungi. Therefore, to reduce microbial contamination of Dutch coffee, managing hygiene while maintaining the refrigeration temperature from the bean management stage to the sale process is crucial.

DIRICHLET FORMS, DIRICHLET OPERATORS, AND LOG-SOBOLEV INEQUALITIES FOR GIBBS MEASURES OF CLASSICAL UNBOUNDED SPIN SYSTEM

  • Lim, Hye-Young;Park, Yong-Moon;Yoo, Hyun-Jae
    • Journal of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.731-770
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    • 1997
  • We study Diriclet forms and related subjects for the Gibbs measures of classical unbounded sping systems interacting via potentials which are superstable and regular. For any Gibbs measure $\mu$, we construct a Dirichlet form and the associated diffusion process on $L^2(\Omega, d\mu), where \Omega = (R^d)^Z^\nu$. Under appropriate conditions on the potential we show that the Dirichlet operator associated to a Gibbs measure $\mu$ is essentially self-adjoint on the space of smooth bounded cylinder functions. Under the condition of uniform log-concavity, the Gibbs measure exists uniquely and there exists a mass gap in the lower end of the spectrum of the Dirichlet operator. We also show that under the condition of uniform log-concavity, the unique Gibbs measure satisfies the log-Sobolev inequality. We utilize the general scheme of the previous works on the theory in infinite dimensional spaces developed by e.g., Albeverio, Antonjuk, Hoegh-Krohn, Kondratiev, Rockner, and Kusuoka, etc, and also use the equilibrium condition and the regularity of Gibbs measures extensively.

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ON A POSITIVE SUBHARMONIC BERGMAN FUNCTION

  • Kim, Jung-Ok;Kwon, Ern-Gun
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.623-632
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    • 2010
  • A holomorphic function F defined on the unit disc belongs to $A^{p,{\alpha}}$ (0 < p < $\infty$, 1 < ${\alpha}$ < $\infty$) if $\int\limits_U|F(z)|^p \frac{1}{1-|z|}(1+log)\frac{1}{1-|z|})^{-\alpha}$ dxdy < $\infty$. For boundedness of the composition operator defined by $C_{fg}=g{\circ}f$ mapping Blochs into $A^{p,{\alpha}$ the following (1) is a sufficient condition while (2) is a necessary condition. (1) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha}M_p(r,\lambda{\circ}f)^p\;dr$ < $\infty$ (2) $\int\limits_o^1\frac{1}{1-r}(1+log\frac{1}{1-r})^{-\alpha+p}(1-r)^pM_p(r,f^#)^p\;dr$ < $\infty$.