θ-Summation and Hardy Spaces

Journal of Approximation Theory

Volumn 107, Issue 1, 2000, Pages 121-142

  Weisz, Ferenc ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

summation; Atomic decomposition; Fourier transforms; Hardy spaces; Interpolation; P atom

Indexed keywords

EID: 0002663341     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.2000.3505     Document Type: Article

References (23)

1. Bari N. K. Trigonometric Series. 1961;Fizmatgiz, Moskva.
2. Bokor J., Schipp F. Approximate identification in Laguerre and Kautz bases. Automatica. 34:1998;463-468.
3. Butzer P. L., Nessel R. J. Fourier Analysis and Approximation. 1971;Birkhäuser, Basel.
4. p spaces the real method. Trans. Amer. Math. Soc. 191:1974;75-81.
5. p spaces of several variables. Acta Math. 129:1972;137-194.
6. Gevorkyan G. G. On the uniqueness of trigonometric series. Mat. Sb. 180:1989;1462-1474.
7. Gevorkyan G. G. On the trigonometric series that are summable by Riemann's method. Mat. Zametki. 52:1992;17-34.
8. Long R. Martingale Spaces and Inequalities. 1993;Peking University Press and Vieweg.
9. Marcinkiewicz J., Zygmund Z. On the summability of double Fourier series. Fund. Math. 32:1939;122-132.
10. Móricz F. The maximal Fejér operator for Fourier transforms of functions in Hardy spaces. Acta Sci. Math. (Szeged). 62:1996;537-555.
11. ∞ system approximation algorithms generated by φ summations. Automatica. 33:1997;2019-2024.
12. ∞-norm. Approximation Theory and Function Series. 1996;Bolyai Soc. Math. Studies, Budapest. p. 307-320.
13. Schipp F., Wade W. R., Simon P., Pál J. Walsh Series: An Introduction to Dyadic Harmonic Analysis. 1990;Hilger, Bristol/New York.
14. Stein E. M., Weiss G. Introduction to Fourier Analysis on Euclidean Spaces. 1971;Princeton Univ. Press, Princeton.
15. Stein E. M. Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals. 1993;Princeton Univ. Press, Princeton.
16. L. Szili, and, P. Vértesi, On uniform convergence of sequences of certain linear operators, Acta Math. Hungar, to appear.
17. L. Szili, On the summability of trigonometric interpolation processes, Acta Math. Hungar, to appear.
18. Torchinsky A. Real-Variable Methods in Harmonic Analysis. 1986;Academic Press, New York.
19. Weisz F. Martingale Hardy Spaces and Their Applications in Fourier-Analysis. Lecture Notes in Mathematics. 1568:1994;Springer-Verlag, Berlin.
20. Weisz F. Riemann summability of two-parameter trigonometric-Fourier series. East J. Approx. 3:1997;403-418.
21. Weisz F. Riesz means of Fourier transforms and Fourier series on Hardy spaces. Studia Math. 131:1998;253-270.
22. Wiener N. The Fourier Integral and Certain of Its Applications. 1959;Dover, New York.
23. Zygmund A. Trigonometric Series. 1959;Cambridge Press, London.