• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.29-36
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• 1995

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.43-46
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• 2018

It is concerned with the continuity of the Hardy-Little wood maximal function between the classical Lebesgue spaces or the Orlicz spaces. A new approach to the continuity of the Hardy-Littlewood maximal function is presented through the observation that the continuity is closely related to the existence of solutions for a certain type of first order ordinary differential equations. It is applied to verify the continuity of the Hardy-Littlewood maximal function from $L^p({\mathbb{R}}^n)$ to $L^q({\mathbb{R}}^n)$ for 1 ${\leq}$ q < p < ${\infty}$.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.93-100
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• 2001

Author proves weak type estimates of the maximal function associated with the Bochner-Riesz means while it is claimed p=2n/(n+1+$2\delta) and 0<\delta\leq(n-1)/2$ that the maximal function is bounded on L^p-{rad}$.

• Journal of Korean Physical Therapy Science
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• v.23 no.1
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• pp.1-8
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• 2016

Purpose : The purpose of this study was to investigate the response of pulmonary function and heart rate recovery of smoker and nonsmoker in males aged 20s after graded maximal exercise. Method : The subjects were composed of smoker group (n=12) and nonsmoker group (n=12) in males aged 20s. Each groups completed an graded maximal exercise with Bruce protocol and were assessed on the pulmonary function(forced vital capacity : FVC, forced expiratory volume-one second : FEV1, FEV1/FVC) and heart rate. Result : The results were as follows: First, heart rate in the measurement point was a statistically significant difference for smoker and non-smoker group after maximal exercise, but FVC, FEV1, FEV1/FVC was no difference. Second, FEV1/FVC between smoker and nonsmoker group was a statistically significant difference after maximal exercise, but FVC, FEV1, heart rate was no difference. Conclusion : The results of this study is that smoking is negative effects on FEV1/FVC of pulmonary function in males aged 20s after maximal exercise.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1391-1408
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• 2023

Let M and M^# be Hardy-Littlewood maximal operator and sharp maximal operator, respectively. In this article, we present necessary and sufficient conditions for the boundedness properties for commutator operators [M, b] and [M^#, b] in a general context of Banach function spaces when b belongs to BMO(?ⁿ) spaces. Some applications of the results on weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces and Musielak-Orlicz spaces are also given.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.371-381
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• 1997

Our basic concern in this paper is to investigate some geometric properties of the graph of a maximal monotone operator in the one dimensional case. Using a well-known theorem of Minty, we answer S. Simon's questions affirmatively in the one dimensional case. Further developments of these results are also treated. In addition, we provide a new proof of Rockafellar's characterization of maximal monotone operators on R: every maximal monotne operator from R to $2^R$ is the subdifferential of a proper convex lower semicontinuous function.

• The Journal of Korean Physical Therapy
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• v.12 no.3
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• pp.379-386
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• 2000

This study is aimed to determine the cardiovascular function response to maximal exercise of chronic low back pain patients(N=13) and normal group(N=13). by using BRUCE PROTOCOL, subjects underwent tredmill exercise test. Their cardiovascular function responses during rest and after maximal exercise were compared The responses were analyzed using t-test for SPSS 7.0 program. The Cardiovascular function variables employed at rest time(Vo2, HR. Vo2/kg, VE, Vco2.) and all out time(Vo2peak. HRpeak, Vo2peak/kg, VEpeak. Vco2peak). Result show that : 1 There was no significant difference in Vo2 between chronic low back pain patients and normal group at rest time. However significant difference in Volpeak was observed after maximal exercise( p<.05). 2. There was no significant difference in HR between chronic low back pain patients and normal group at rest time. No significant difference in HRpeak likewise observed. 3. There was no significant difference in Vo2/kg between chronic low back pain patients and normal group at rest time. However significant difference in Vo2peak/kg was observed after maximal exercise load(p<.05). 4. There was no significance in VE between chronic low bark pain patients and normal group at rest time. However significant difference in VEpeak observed after maximal exercise load(p<.05).

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.155-162
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• 1995

Let $\mu$ be a positive Borel measure on $R^n$ which is positive on cubes. For any cube $Q \subset R^n$, a Borel measurable nonnegative function $\varphi_Q$, supported and positive a.e. with respect to $\mu$ in Q, is given. We consider a maximal function $$ M_{\mu}f(x) = sup \int \varphi Q$\mid$f$\mid$d_{\mu} $$ where the supremum is taken over all $\varphi Q$ such that $x \in Q$.

• 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 Data and Information Science Society
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• v.19 no.4
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• pp.1091-1100
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• 2008

The purpose of this study is to find out how energy substrate's utilizations in the maximal exercise-cardiorespiratory function and the energy metabolic variation- have the effect on before and after the supplements of coenzyme Q10(100mg per day for 8 weeks) based on the male students(CoQ10=8, placebo=8) of high school. The results of this study are as follows: Maximal oxygen uptake and maximal oxygen per weight are found to have the significant increase respectively in supplement group. Glucose is found to have the significant decrease after the supplement of CoQ10. And then FFA is found to have the significant increase. In the above results, the supplements of CoQ10 and cardiorespiratory function in the maximal exercise are found to have the improvement. CoQ10 in the anaerobic exercise spares the energy's utilization of Glucose and then is found to have the increase of the utilization of FFA. CoQ10 in the aerobic exercise is reported to have the increase of the utilization of FFA and then CoQ10 in the maximal exercise is also recognized to have the increase of the utilization of FFA, or energy substrates.