Riesz means of Fourier transforms and Fourier series on Hardy spaces

Studia Mathematica

Volumn 131, Issue 3, 1998, Pages 253-270

  Weisz, Ferenc ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

Atomic decomposition; Fourier transforms; Hardy spaces; Interpolation; P atom; Riesz means

Indexed keywords

EID: 0002401284     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm-131-3-253-270     Document Type: Article

References (17)

1. C. Bennett and R. Sharpley, Interpolation of Operators, Pure Appl. Math. 129, Academic Press, New York, 1988.
2. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976.
3. p, Trans. Amer. Math. Soc. 157 (1971), 137-153.
4. P. L. Butzer and R. J. Nessel, Fourier Analysis and Approximation, Birkhäuser, Basel, 1971.
5. p spaces: the real method, Trans. Amer. Math. Soc. 191 (1974), 75-81.
6. p spaces of several variables, Acta Math. 129 (1972), 137-193.
7. B. S. Kashin and A. A. Saakjan, Orthogonal Series, Transl. Math. Monographs 75, Amer. Math. Soc., 1989.
8. J. Marcinkiewicz and A. Zygmund, On the summability of double Fourier series, Fund. Math. 32 (1939), 122-132.
9. 1, in: Approximation Theory and Function Series (Budapest, 1995), Bolyai Soc. Math. Stud. 5, Budapest, 1996, 275-292.
10. 1, the real method, J. Funct. Anal. 14 (1973), 401-409.
11. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
12. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971.
13. F. Weisz, Cesàro summability of one-and two-dimensional trigonometric-Fourier series, Colloq. Math. 74 (1997), 123-133.
14. _, Martingale Hardy Spaces and Their Applications in Fourier-Analysis, Lecture Notes in Math. 1568, Springer, Berlin, 1994.
15. _, The maximal Fejér operator of Fourier transforms on Hardy spaces, Acta Sci. Math. (Szeged), to appear.
16. N. Wiener, The Fourier Integral and Certain of Its Applications, Dover, New York, 1959.
17. A. Zygmund, Trigonometric Series, Cambridge Univ. Press, London, 1959.