Spaces of functions of generalized bounded variation. I. Embedding theorems. Estimates for lebesgue constants
Article
Received:
Revised:
- 41 Downloads
- 2 Citations
Keywords
Fourier Series Orlicz Space Lorentz Space Ideal Space Variation Modulus
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.N. Wiener, “The quadratic variation of a function and its Fourier coefficients,” Massachusetts J. Math., No.3, 72–94 (1924).Google Scholar
- 2.L. C. Young, “Sur une generalization de la notion de variation de poissancep-ieme bornee au sence de N. Wiener, et sur la convergence des series de Fourier,” C. R. Acad. Sci. Paris Sér. I Math.,204, 470–472 (1937).MATHGoogle Scholar
- 3.Z. A. Chanturiya, “On uniform convergence of Fourier series,” Mat. Sb.,100, No. 4, 534–554 (1976).Google Scholar
- 4.D. Waterman, “On convergence of Fourier series of functions of generalized variation,” Studia Math.,44, 107–112 (1972).MATHGoogle Scholar
- 5.D. Waterman, “On Λ-bounded variation,” Studia Math.,57, 33–45 (1976).MATHGoogle Scholar
- 6.S. Perlman, “Functions of generalised variation,” Fund. Math.,105, 200–211 (1980).Google Scholar
- 7.M. Schramm and D. Waterman, “On the magnitude of Fourier coefficients,” Proc. Amer. Math. Soc.,85, 407–410 (1982).MATHCrossRefGoogle Scholar
- 8.E. I. Berezhnoî, “An exact refinement theorem for the spaces of functions of generalized bounded variation,” Mat. Zametki,56, No. 5, 10–21 (1994).Google Scholar
- 9.A. S. Belov, “Relations between different classes of functions of generalized bounded variation,” in: Reports of Extended Seminars of the I. N. Vekua Institute, 1988,3, No. 2, 11–14.Google Scholar
- 10.A. Avdispanic, “On the classesΛBV andV(v),” Proc. Amer. Math. Soc.,95, No. 2, 230–234 (1985).CrossRefGoogle Scholar
- 11.J. Ciemnocrolowski and W. Orlicz, “Inclusion theorems for classes of functions of generalized bounded variation,” Comment. Math. Ser. I,24, No. 2, 181–184 (1984).Google Scholar
- 12.S. Perlman and D. Waterman, “Some remarks of functions of Λ-bounded variation,” Proc. Amer. Math. Soc.,74, No. 1, 113–118 (1979).MATHCrossRefGoogle Scholar
- 13.A. P. Terekhin, “The Lebesgue constant for the space of functions of boundedp-variation,” Mat. Zametki,2, No. 3, 289–300 (1967).MATHGoogle Scholar
- 14.E. I. Berezhnoî, “Fourier series for functions of generalized bounded variation,” in: Abstracts: All-Union School on Approximate Theory, Lutsk, 1989.Google Scholar
- 15.S. G. Kreîn, Yu. I. Petunin, and E. M. Semënov, Interpolation of Linear Operators, [in Russian], Nauka, Moscow (1977).Google Scholar
- 16.J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. Vol. 1 and 2: Function Spaces, Springer-Verlag, Berlin (1979).Google Scholar
- 17.P. P. Zabreîko, “Ideal spaces of functions,” Vestnik Yaroslavsk. Univ., No.8, 12–52 (1974).Google Scholar
- 18.M. A. Krasnosel'skiî and Ya. B. Rutitskiî, Convex Functions and Orlicz Spaces [in Russian], Fizmatgiz, Moscow (1958).Google Scholar
- 19.Z. A. Chanturiya, “On dependence between the classesV ϕ andV[v],” Soobshch. Akad. Nauk Gruzin. SSR,131, No. 2, 253–255 (1988).MATHGoogle Scholar
- 20.A. Zygmund, Trigonometric Series. Vol. 1 and 2 [Russian translation], Mir, Moscow (1965).Google Scholar
- 21.S. M. Nikol'skiî, “The Fourier series of a function with a prescribed continuity modulus,” Dokl. Akad. Nauk SSSR,52, No. 3, 191–194 (1946).Google Scholar
Copyright information
© Kluwer Academic/Plenum Publishers 1999