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Approximation of Fourier series in terms of functions in $L_p$ Spaces for 0 | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 897-911 اصل مقاله (420.3 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5146 | ||
| نویسندگان | ||
| Sahab Mohsen Aboud؛ Eman Samir Bhaya* | ||
| Mathematics Department, College of Education for pure Sciences, University of Babylon, Babylon, Iraq | ||
| تاریخ دریافت: 18 اسفند 1399، تاریخ بازنگری: 05 اردیبهشت 1400، تاریخ پذیرش: 14 اردیبهشت 1400 | ||
| چکیده | ||
| Many results introduced for the absolutely convergence of Fourier series in terms of absolutely continuous functions. Here we study the convergence of Fourier series in terms of $p$-integrable functions series. | ||
| کلیدواژه‌ها | ||
| modulus of continuity؛ Dyadic intervals؛ Haar system؛ Rademacher system | ||
| مراجع | ||
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[1] S. Kaczmarz and H. Steinhaus, Theorie der orthogonalreihen, Monografie Mat., Tom 6, PWN, Warsaw, 1935; reprint, Chelsea, New York, 1951; Russian transl., Fizmatgiz, Moscow, 1958. [2] P· Kahane, Series de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin and New York, 1970. [3] R. Salem, On a theorem of Zygmund, Duke Math. J. 10 (1943) 23–31. [4] Y. Ul’yanov, P. Lavrent’evich, Solved and unsolved problems in the theory of trigonometric and orthogonal series, Russian Math. Sur. 19 (1964) 1–62. [5] S. Vo Bockarev, On a problem of Zygmund, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 630–638. [6] I. Wik, Criteria for absolute convergence of Fourier series of functions of bounded variation, Trans. Amer. Math. Soc. 163 (1971) 1–24. [7] S. Yano, On a lemma of Marcinkiewicz and its applications to Fourier series, Tohoku Math. J. 2 (1959) 191–215. [8] A. Zygmund, Remarque sur la convergence absolue des s´eries de Fourier, J. London Math. Soc. 1 (1928) 194–196. | ||
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