Lp(T2)-수렴성과 모리츠에 관하여
On Lp(T2)-ConvergenceandMóricz
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
본 논문에서는 20세기 후반부터 현재까지 이중 푸리에 급수와 이중 삼각계 급수의 수렴성에 관하여 페렌츠 모리츠의 연구를 중심으로 주목할만한 결과들을 순차적으로 살펴본다. 특히 모리츠의 $L^p (T^2 )$-수렴성 연구결과들 중 몇가지 특징을 고찰한다. 결론으로 푸리에부터 모리츠까지 그의 학문적 계보를 조사하여 밝히고 그의 연구경향과 $L^p (T^2 )$-수렴성 연구 소계보를 작성하여 제시한다.
Abstract
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 Móricz has studied the convergence of double trigonometric series and double Fourier series so far. We consider Lp(T2)-convergence results focused on the Ferenc Móricz’s studies from the second half of the 20th century up to now. In section 2, we reintroduce some of Ferenc Móricz’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 Móricz. In addition, we present the research minor lineage of his study on Lp(T2)-convergence.
참고문헌 (15)
- Chang-Pao Chen, "Pointwise convergence of multiple trigonometric series", J. Math. Anal. Appl, 185(3), pp.629~646 (1994)
- X. Z. Krasniqi, "Necessary conditions for the Lp-convergence (0 <p < 1) of single and double trigonometric series", Mathematica Bohemica, 139(1), pp.75~88 (2014)
- L. Krizsan, "The Lebesque summability of double triginometric integrals", Mathematical Inequalities & Applications, 17(4), pp.1543~1550 (2014)
- 이정오, "바티의 L1-수렴성 연구에 관한 소고", 한국수학사학회지, 27(1), pp.81~93 (2014), 한국수학사학회[DOI]
- 이정오, "이중 푸리에 급수의 총합가능성과 수렴성에 대한 고전적인 연구들에 관하여", 한국수학사학회지, 27(4), pp.285~297 (2014), 한국수학사학회[DOI]
- F. Móricz, "Convergence and integrability of double trigonometric series with coefficients of bounded variation", Proc. Am. Math. Soc, 102(3), pp.633~640 (1988)
- F. Móricz, "On the integrability of double cosine and sine series. I", J. Math. Anal. Appl, 154(2), pp.452~465 (1991)
- F. Móricz, "On the integrability of double cosine and sine series. II", J. Math. Anal. Appl, 154(2), pp.466~483 (1991)
- F. Móricz, "L1-convergence of double Fourier series", Journal of Mathematical Analysis and Applications, 186, pp.209~236 (1994)
- F. Móricz, "On the maximal Fejér operator for double Fourier series of functions in Hardy spaces", Stud. Math, 116(1), pp.89~100 (1995)
- F. Móricz, "Necessary conditions for L1-convergence of double Fourier series", J. Math. Anal. Appl, 363, pp.559~568 (2010)
- F. Móricz, "On the Lebesgue summability of double trigonometric series", J. Math. Anal. Appl, 348, pp.555~561 (2008)
- F. Móricz, "Approximation by Nörlund means of double Fourier series for Lipschitz functions", J. Approximation Theory, 50, pp.341~358 (1987)
- F. Móricz, "Approximation to continuous functions by Cesàro means of double Fourier series and conjugate series", J. Approximation Theory, 49, pp.346~377 (1987)
- F. Móricz, "Convergence of double Fourier series with coefficients of generalized bounded variation", J. Math. Anal. Appl, 140(1), pp.34~49 (1989)