Some classical function systems in separable Orlicz spaces

C. Finet; G. Tkebuchava

Studia Mathematica (1996)

  • Volume: 121, Issue: 2, page 193-205
  • ISSN: 0039-3223

Abstract

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The boundedness of (sub)sequences of partial Fourier and Fourier-Walsh sums in subspaces of separable Orlicz spaces is studied. The boundedness of the shift operator and Paley function with respect to the Haar system is also investigated. These results are applied to get the analogues of the classical theorems on basicness of the trigonometric and Walsh systems in nonreflexive separable Orlicz spaces.

How to cite

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Finet, C., and Tkebuchava, G.. "Some classical function systems in separable Orlicz spaces." Studia Mathematica 121.2 (1996): 193-205. <http://eudml.org/doc/216351>.

@article{Finet1996,
abstract = {The boundedness of (sub)sequences of partial Fourier and Fourier-Walsh sums in subspaces of separable Orlicz spaces is studied. The boundedness of the shift operator and Paley function with respect to the Haar system is also investigated. These results are applied to get the analogues of the classical theorems on basicness of the trigonometric and Walsh systems in nonreflexive separable Orlicz spaces.},
author = {Finet, C., Tkebuchava, G.},
journal = {Studia Mathematica},
keywords = {Fourier; Fourier-Walsh series; Paley function; Haar system; separable Orlicz space; Walsh series; Haar series; bases in Orlicz spaces; Walsh-Fourier series; Walsh system; Haar shift operator; Haar-Paley function; maximal function; Haar-Fourier series},
language = {eng},
number = {2},
pages = {193-205},
title = {Some classical function systems in separable Orlicz spaces},
url = {http://eudml.org/doc/216351},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Finet, C.
AU - Tkebuchava, G.
TI - Some classical function systems in separable Orlicz spaces
JO - Studia Mathematica
PY - 1996
VL - 121
IS - 2
SP - 193
EP - 205
AB - The boundedness of (sub)sequences of partial Fourier and Fourier-Walsh sums in subspaces of separable Orlicz spaces is studied. The boundedness of the shift operator and Paley function with respect to the Haar system is also investigated. These results are applied to get the analogues of the classical theorems on basicness of the trigonometric and Walsh systems in nonreflexive separable Orlicz spaces.
LA - eng
KW - Fourier; Fourier-Walsh series; Paley function; Haar system; separable Orlicz space; Walsh series; Haar series; bases in Orlicz spaces; Walsh-Fourier series; Walsh system; Haar shift operator; Haar-Paley function; maximal function; Haar-Fourier series
UR - http://eudml.org/doc/216351
ER -

References

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  16. [16] Ryan R., Conjugate functions in Orlicz spaces, Pacific J. Math. 13 (1963), 1371-1377. Zbl0133.37301
  17. [17] Tkebuchava G. E., On unconditional bases in nonreflexive function spaces, Soobshch. Akad. Nauk Gruzin. SSR 101 (2) (1981), 297-299 (in Russian); English transl. in: Fifteen Papers on Functional Analysis, Amer. Math. Soc. Transl. (2) 124, 1984, 17-19. Zbl0455.46026
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