Sequences of bounded φ-variation and weighted unconditional convergence of series

• Autorzy: Musielak J.
• Języki publikacji: EN

Abstrakty

EN

There are investigated spaces v0,φ of sequences of bounded φ-variation. Spaces v0, φ are applied to the problem of weighted unconditional convergence of series. It is shown that (vo,φ,lφ* ), where lφ* means the Orlicz sequence space generated by the N-function φ*, is a pair of weighted unconditional convergence. There are also considered nonlinear convolution - type operators in v0,φ .

Słowa kluczowe

EN

sequence of bounded φ-variation; Orlicz sequence space; unconditionally convergent series; convolution type operator

PL

operatory; przestrzeń Orlicza; ciągi ograniczone

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 153--162
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Musielak J.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland

Bibliografia

• [1] C. Bardaro, J. Musielak and G. Vinti, Nonlinear integral operators and applications, de Gruyter Series in Nonlinear Analysis and Applications 9, Berlin, New York 2003.
• [2] Z. W. Birnbaum and W. Orlicz, Über die Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen, Studia Math. 3 (1931), 1-67.
• [3] J. Musielak, Sequences of finite M-variation, Prace Mat. 6 (1961), 165-174 (in Polish).
• [4] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics 1034, Springer Verlag, Berlin, Heidelberg, New York, Tokyo (1983).
• [5] J. Musielak and W. Orlicz, On generalized variations (I), Studia Math. 18 (1959), 11-41.
• [6] J. Musielak and W. Orlicz, On modular spaces, Studia Math. 18 (1959), 49-65.
• [7] J. Musielak and A. Waszak, Generalized variation and translation operator in some sequence spaces, Hokkaido Math. J. 17 (1988), 345-353.
• [8] L. C. Young, General inequalities for Stieltjes integrals and the convergence of Fourier series, Math. Ann. 115 (1938), 581-612.