• 제목/요약/키워드: Area integral function

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Weighted Lp Boundedness for the Function of Marcinkiewicz

  • Al-Qassem, Hussain M.
    • Kyungpook Mathematical Journal
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    • 제46권1호
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    • pp.31-48
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    • 2006
  • In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

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WEIGHTED ESTIMATES FOR ROUGH PARAMETRIC MARCINKIEWICZ INTEGRALS

  • Al-Qassem, Hussain Mohammed
    • 대한수학회지
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    • 제44권6호
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    • pp.1255-1266
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    • 2007
  • We establish a weighted norm inequality for a class of rough parametric Marcinkiewicz integral operators $\mathcal{M}^{\rho}_{\Omega}$. As an application of this inequality, we obtain weighted $L^p$ inequalities for a class of parametric Marcinkiewicz integral operators $\mathcal{M}^{*,\rho}_{\Omega,\lambda}\;and\;\mathcal{M}^{\rho}_{\Omega,S}$ related to the Littlewood-Paley $g^*_{\lambda}-function$ and the area integral S, respectively.

2015 개정 교육과정에 따른 <수학II> 교과서의 정적분의 도입 및 활용 분석 (An analysis of the introduction and application of definite integral in textbook developed under the 2015-Revised Curriculum)

  • 박진희;박미선;권오남
    • 한국수학교육학회지시리즈A:수학교육
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    • 제57권2호
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    • pp.157-177
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    • 2018
  • The students in secondary schools have been taught calculus as an important subject in mathematics. The order of chapters-the limit of a sequence followed by limit of a function, and differentiation and integration- is because the limit of a function and the limit of a sequence are required as prerequisites of differentiation and integration. Specifically, the limit of a sequence is used to define definite integral as the limit of the Riemann Sum. However, many researchers identified that students had difficulty in understanding the concept of definite integral defined as the limit of the Riemann Sum. Consequently, they suggested alternative ways to introduce definite integral. Based on these researches, the definition of definite integral in the 2015-Revised Curriculum is not a concept of the limit of the Riemann Sum, which was the definition of definite integral in the previous curriculum, but "F(b)-F(a)" for an indefinite integral F(x) of a function f(x) and real numbers a and b. This change gives rise to differences among ways of introducing definite integral and explaining the relationship between definite integral and area in each textbook. As a result of this study, we have identified that there are a variety of ways of introducing definite integral in each textbook and that ways of explaining the relationship between definite integral and area are affected by ways of introducing definite integral. We expect that this change can reduce the difficulties students face when learning the concept of definite integral.

INTRINSIC SQUARE FUNCTIONS ON FUNCTIONS SPACES INCLUDING WEIGHTED MORREY SPACES

  • Feuto, Justin
    • 대한수학회보
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    • 제50권6호
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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.

A NOTE ON THE W*IN DUAL SPACE

  • Yoon, Ju-Han
    • 대한수학회보
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    • 제33권2호
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    • pp.277-287
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    • 1996
  • The theory of integration of functions with values in a Banach space has long been a fruitful area of study. In the eight years from 1933 to 1940, seminal papers in this area were written by Bochner, Gelfand, Pettis, Birhoff and Phillips. Out of this flourish of activity, two integrals have proved to be of lasting: the Bochner integral of strongly measurable function. Through the forty years since 1940, the Bochner integral has a thriving prosperous history. But unfortunately nearly forty years had passed until 1976 without a significant improvement after B. J. Pettis's original paper in 1938 [cf. 11].

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EDI방법에 의한 유한요소모델의 J-적분값 산정 (Evaluation of J-integrals by Finite Element Model Based on EDI Method)

  • 신성진;홍종현;우광성
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 1996년도 봄 학술발표회 논문집
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    • pp.62-69
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    • 1996
  • In this study, an equivalent domain integral (EDI) method is presented to estimate the track-till integral parameter, J-value, for two dimensional cracked elastic bodies which may quantify the severity of the crack-tit) stress fields. The conventional J-integral method based on line integral has been converted to equivalent area or domain integrals by using the divergence theorem. It is noted that the EDI method is very attractive because all the quantities necessary for computation of the domain integrals are readily available in a finite element analysis. The details and its implementation are extened to both h-version finite element model with 8-node isoparametric element and p-version finite element model with high order hierarchic element using Legendre type shape fuctions. The variations with respect to the different path of domain integrals from the crack-tip front and the choice of 5-function have been tested by several examples.

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아르키메데스의 《The Method》의 해석기하학적 특성과 그 교육적 시사점에 대한 연구 (A study on the analytic geometric characteristics of Archimedes' 《The Method》 and its educational implications)

  • 박선용
    • 한국수학사학회지
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    • 제27권4호
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    • pp.271-283
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    • 2014
  • This study takes a look at Polya's analysis on Archimedes' "The Method" from a math-historical perspective. We, based on the elaboration of Polya's analysis, investigate the analytic geometric characteristics of Archimedes' "The Method" and discuss the way of using the characteristics in education of school calculus. So this study brings up the educational need of approach of teaching the definite integral by clearly disclosing the transition from length, area, volume etc into the length as an area function under a curve. And this study suggests the approach of teaching both merit and deficiency of the indivisibles method, and the educational necessity of making students realizing that the strength of analytic geometry lies in overcoming deficiency of the indivisibles method by dealing with the relation of variation and rate of change by means of algebraic expression and graph.

SPATIAL BEHAVIOR OF SOLUTION FOR THE STOKES FLOW EQUATION

  • Liu, Yan;Liao, Wenhui;Lin, Changhao
    • 대한수학회보
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    • 제48권2호
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    • pp.397-412
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    • 2011
  • In this paper, the equation of the transient Stokes flow of an incompressible viscous fluid is studied. Growth and decay estimates are established associating some appropriate cross sectional line and area integral measures. The method of the proof is based on a first-order differential inequality leading to an alternative of Phragm$\'{e}$n-Lindell$\"{o} $f type in terms of an area measure of the amplitude in question. In the case of decay, we also indicate how to bound the total energy.