한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
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Lp(T2)-수렴성과 모리츠에 관하여

On Lp(T2)-Convergence and Móricz

  • LEE, Jung Oh (Dept. of liberal arts, Chosun College of Science and Technology)
  • 투고 : 2015.10.27
  • 심사 : 2015.12.11
  • 발행 : 2015.12.31
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초록

This paper is concerned with the convergence of double trigonometric series and Fourier series. Since the beginning of the 20th century, many authors have studied on those series. Also, Ferenc $M{\acute{o}}ricz$ has studied the convergence of double trigonometric series and double Fourier series so far. We consider $L^p(T^2)$-convergence results focused on the Ferenc $M{\acute{o}}ricz^{\prime}s$ studies from the second half of the 20th century up to now. In section 2, we reintroduce some of Ferenc $M{\acute{o}}ricz^{\prime}s$ remarkable theorems. Also we investigate his several important results. In conclusion, we investigate his research trends and the simple minor genealogy from J. B. Joseph Fourier to Ferenc $M{\acute{o}}ricz$. In addition, we present the research minor lineage of his study on $L^p(T^2)$-convergence.

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참고문헌

  1. Chang-Pao CHEN, Hui-Chuan WU, F. MORICZ, Pointwise convergence of multiple trigonometric series., J. Math. Anal. Appl. 185(3) (1994), 629-646. https://doi.org/10.1006/jmaa.1994.1273
  2. X. Z. KRASNIQI, P. KORUS, F. MORICZ, Necessary conditions for the $L^p$-convergence (0 < p < 1) of single and double trigonometric series., Mathematica Bohemica 139(1) (2014), 75-88.
  3. L. KRIZSAN, F. MORICZ, The Lebesque summability of double triginometric integrals, Mathematical Inequalities & Applications 17(4) (2014), 1543-1550.
  4. LEE Jung Oh , A brief study on Bhatia's research of $L^1$-convergence, The Korean Journal for History of Mathematics 27(1) (2014), 81-93. https://doi.org/10.14477/jhm.2014.27.1.081
  5. LEE Jung Oh, On Classical Studies for the Summability and Convergence of Double Fourier Series, The Korean Journal for History of Mathematics, 27(4) (2014), 285-297. https://doi.org/10.14477/jhm.2014.27.4.285
  6. F. MORICZ, Convergence and integrability of double trigonometric series with coefficients of bounded variation, Proc. Am. Math. Soc.102(3) (1988), 633-640. https://doi.org/10.1090/S0002-9939-1988-0928995-2
  7. F. MORICZ, On the integrability of double cosine and sine series. I., J. Math. Anal. Appl. 154(2) (1991), 452-465. https://doi.org/10.1016/0022-247X(91)90050-A
  8. F. MORICZ, On the integrability of double cosine and sine series. II., J. Math. Anal. Appl. 154(2) (1991), 466-483. https://doi.org/10.1016/0022-247X(91)90051-Z
  9. F. MORICZ, $L^1$-convergence of double Fourier series., Journal of Mathematical Analysis and Applications 186 (1994), 209-236. https://doi.org/10.1006/jmaa.1994.1295
  10. F. MORICZ, On the maximal Fejer operator for double Fourier series of functions in Hardy spaces., Stud. Math. 116(1) (1995), 89-100. https://doi.org/10.4064/sm-116-1-89-100
  11. F. MORICZ, Necessary conditions for $L^1$-convergence of double Fourier series, J. Math. Anal. Appl. 363 (2010), 559-568. https://doi.org/10.1016/j.jmaa.2009.09.030
  12. F. MORICZ, M. BAGOTA, On the Lebesgue summability of double trigonometric series, J. Math. Anal. Appl. 348 (2008), 555-561. https://doi.org/10.1016/j.jmaa.2008.07.064
  13. F. MORICZ, B. E. RHOADES, Approximation by Norlund means of double Fourier series for Lipschitz functions, J. Approximation Theory 50 (1987), 341-358. https://doi.org/10.1016/0021-9045(87)90012-8
  14. F. MORICZ, Shi, Xianliang, Approximation to continuous functions by Cesaro means of double Fourier series and conjugate series, J. Approximation Theory 49 (1987), 346-377. https://doi.org/10.1016/0021-9045(87)90074-8
  15. F. MORICZ, Daniel WATERMAN, Convergence of double Fourier series with coefficients of generalized bounded variation., J. Math. Anal. Appl. 140(1) (1989), 34-49. https://doi.org/10.1016/0022-247X(89)90092-9

피인용 문헌

  1. 푸리에 급수에 대한 체사로 총합가능성의 고전적 결과에 관하여 vol.30, pp.1, 2017, https://doi.org/10.14477/jhm.2017.30.1.017
  2. 푸리에 급수에 대한 총합가능성의 결과들에 관하여 vol.30, pp.4, 2015, https://doi.org/10.14477/jhm.2017.30.4.233