Hardy Spaces on the Plane and Double Fourier Transforms

Journal of Fourier Analysis and Applications

Volumn 2, Issue 5, 1996, Pages

  Giang, Dang Vu ^a   Móricz, Ferenc ^b  

^a UNIVERSITY OF PANNONIA   (Hungary)

^b UNIVERSITY OF SZEGED   (Hungary)

Author keywords

Absolute continuity; Conjugate functions; Conjugate series; Double fourier series; Double null sequence of bounded variation; Fourier transform; Hardy inequality; Hardy space; Hilbert transform; Multipliers on l and h; Riesz transform

Indexed keywords

EID: 84951599577     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. Berkson, E., and Gillespie, T. A. (1984). Absolutely continuous functions for two variables and well-bounded operators. J. London Math. Soc. (2) 30, 305-324.
2. 1 and BMO. Adv. Math. 22, 269-277.
3. 1 theory of Fourier transforms and multipliers. Acta Sci. Math. (Szeged), 61, 293-304.
4. _, (1993). Lebesgue intagrability of double Fourier transforms. Acta Sci. Math. (Szeged) 58, 295-324.
5. p theory on product domains II. Function Spaces and Applications, Proc. Conf. Lund 1986. Lecture Notes in Math. 1302, 44-51. Springer, Berlin and Heidelberg.
6. Jawerth, B., and Torchinsky, A. (1986). A note on real interpolation of Hardy spaces in the polydisk. Proc. Amer. Math. Soc. 96, 227-232.
7. Liflyand, E. R. (1993). On asymptotics of Fourier transform for functions of certain classes. Anal. Math. 19, 151-168.
8. 1-convergence of double trigonometric series. Studia Math. 98, 203-225.
9. _, (1993). Lebesgue integrability of double cosine and sine series. Analysis 13, 321-350.
10. n), 0 < p < ∞. Ark. Mat. 17, 225-235.
11. 1 multiplier theorem. Ark. Mat. 19, 265-270.
12. p, multiplicateurs et fonctions de Littlewood-Paley. C. R. Acad. Sci. Paris Sér. I Math. 263, 716-719; 264, 107-108.
13. p, multiplicateurs et fonctions de Littlewood-Paley. C. R. Acad. Sci. Paris Sér. I Math. 263, 716-719; 264, 107-108.
14. _, (1970). Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, N.J.
15. Stein, E. M., and Weiss, G. (1960). On the theory of harmonic functions of several variables. Acta Math. 103, 26-62.
16. _, (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton, N.J.
17. Titchmarsh, E. C. (1937). Introduction to the Theory of Fourier Integrals. Clarendon Press, Oxford.
18. Uchiyama, A. private communication.
19. p spaces of several variables. Acta Math. 129, 137-193.
20. p theory for the poly-disc. Proc. Nat. Acad. Sci. U.S.A. 76, 1026-1029.