A decomposition of Wiener ϕ-variation

• Autorzy: Prus-Wiśniowski, F.
• Języki publikacji: EN

Abstrakty

EN

The pseudomodular fi-variation in the sense of Wiener of a regulated function f is decomposed into sum of two other pseudomodulars, first of which describes the fi-variation given by infinite small changes of f and the second describes fi-variation generated by jumps of f

Słowa kluczowe

EN

bounded fi-variation; modular

• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2003
• Tom: [Z] 43(1)
• Strony: 113-128
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Prus-Wiśniowski, F.

• Instytut Matematyki, Uniwersytet Szczeciński, ul. Wielkopolska 15, 70-392 Szczecin, Poland,

Bibliografia

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• [3] E. Cohen, On the Fourier coefficients and continuity of functions of class VΦ*, Rocky Mountains J. Math. 9 (1979), 227-237.
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• [5] J. Musielak, Orlicz Spaces and Modular Spaces, Lect. Notes in Math. 1034, Springer Verlag 1983.
• [6] J. Musielak and W. Orlicz On generalized variations (I), Studia Math. 18 (1959), 11-41.
• [7] F. Prus-Wiśniowski, Some remarks on functions of bounded ϕ-variation, Comment. Math. Prace Matem. 30 (1990), 147-166.
• [8] F. Prus-Wiśniowski, General properties of functions of bounded λ-variation, Ph.D. Thesis, Syracuse University 1995.
• [9] E. Study, Über eine besondere Classe von Functionen einer reellen Veränderlichen, Math. Ann. 47 (1896) 298-316.
• [10] N. Wiener, The quadratic variation of a function and its Fourier coefficients, J. Math. and Phys. 3(1924), 72-94.
• [11] L. C. Young, General inequalities for Stieltjes integrals and the convergence of Fourier series, Math. Ann. 115 (1938), 581-612.