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Abstrakty
L. Leindler obtained a necessary and sufficient condition in order to a function is an element of Lp having Fourier coefficients of rest bounded variation belong to the Besov class. In the present paper the analogue of this result is proved with function having Fourier coefficients of mean rest bounded variation. We also discuss embedding relations between the Besov classes.
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Czasopismo
Rocznik
Tom
Strony
303--322
Opis fizyczny
Bibliogr. 17 poz.
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autor
- University of Zielona Góra Faculty of Mathematics, Computer Sciences and Econometrics ul. Szafrana 4a 65-516 Zielona Góra, Poland, B.Szal@wmie.uz.zgora.pl
Bibliografia
- [1] N. K. Bari, On best approximation of two conjugate functions by trigonometric polynomials, Izv. Akad. Nauk SSSR Ser. Mat. 19 (1955), 285-302.
- [2] R. P Boas, Jr., Integrability Theorems for Trigonometric Transforms, Springer (Berlin-Heidelberg, 1967).
- [3] G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities, University Press, Cambridge (1934)
- [4] A. A. Konyushkov, Best approximation by trigonometric polynomials and Fourier coefficients, Mat. Sb. 44 (86) (1958), 53-84.
- [5] L. Leindler, Further sharpening of inequalities of Hardy and Littlewood, Acta Sci. Math. 54 (1990), 285-289.
- [6] L. Leindler, A new class of numerical sequences and its applications to sine and cosine series, Analysis Math. 28 (2002), 279-286.
- [7] L. Leindler, Generalization of embedding relations of Besov classes, Analysis Math. 31 (2005), 1-12.
- [8] L. Leindler, A note on the best approximation of sine and cosine series, Analysis Math. 32 (2006), 155-161.
- [9] L. Leindler, Integrability conditions pertaining to Orlicz space, J. Inequal. Pure and Appl. Math. 8 (2) (2007), Art. 38, 6 pp.
- [10] L. Leindler, Embedding results pertaining to strong approximation of Fourier series VI, Acta Sci. Math. (Szeged), 71 (2005), 91-103.
- [11] L. Leindler, Embedding relations of Besov classes, Acta Sci. Math. (Szeged) 73 (2007), 133-149.
- [12] M. K. Potapov, The imbedding and coincidence of certain classes of functions, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 840-860.
- [13] M. K. Potapov, A certain imbedding theorem, Mathematica, 14 (1972), 123-146.
- [14] M. K. Potapov and M. Berisha, Moduli of smoothness and Fourier coefficients of periodic functions of one variable, Publ. de L’institut Math. 26 (1979), 215-228.
- [15] M. Riesz, Sur les fonctions conjuguées, Math. Z. 27 (1927), 218-244.
- [16] B. Szal, A note on the uniform convergence and boundedness a generalized class of sine series, Commentat. Math., in appear.
- [17] M. F. Timan, Peculiarities of fundamental theorems of the constructive theory of functions in the spaces Lp, Studies contemporary problems constructive theory of functions, Izdat. Akad. Nauk Az. SSSR, (Baku 1965).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0024-0009