Discrete Hardy spaces

Santiago Boza; María Carro

Studia Mathematica (1998)

  • Volume: 129, Issue: 1, page 31-50
  • ISSN: 0039-3223

Abstract

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We study various characterizations of the Hardy spaces H p ( ℤ ) via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of H p ( ℤ ) given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.

How to cite

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Boza, Santiago, and Carro, María. "Discrete Hardy spaces." Studia Mathematica 129.1 (1998): 31-50. <http://eudml.org/doc/216490>.

@article{Boza1998,
abstract = {We study various characterizations of the Hardy spaces $H^p(ℤ)$ via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of $H^p(ℤ)$ given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.},
author = {Boza, Santiago, Carro, María},
journal = {Studia Mathematica},
keywords = {Hardy spaces; discrete Hilbert transform; maximal operators},
language = {eng},
number = {1},
pages = {31-50},
title = {Discrete Hardy spaces},
url = {http://eudml.org/doc/216490},
volume = {129},
year = {1998},
}

TY - JOUR
AU - Boza, Santiago
AU - Carro, María
TI - Discrete Hardy spaces
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 1
SP - 31
EP - 50
AB - We study various characterizations of the Hardy spaces $H^p(ℤ)$ via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of $H^p(ℤ)$ given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.
LA - eng
KW - Hardy spaces; discrete Hilbert transform; maximal operators
UR - http://eudml.org/doc/216490
ER -

References

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  1. [AC] P. Auscher and M. J. Carro, On relations between operators on ℝ N , N and ℤ N , Studia Math. 101 (1992), 165-182. 
  2. [B] R. P. Boas, Entire Functions, Academic Press, 1954. Zbl0058.30201
  3. [C] R. Coifman, A real-variable characterization of H p , Studia Math. 51 (1974), 269-274. Zbl0289.46037
  4. [CW] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. Zbl0358.30023
  5. [E] C. M. Eoff, The discrete nature of the Paley-Wiener spaces, Proc. Amer. Math. Soc. 123 (1995), 505-512. Zbl0820.30017
  6. [FS] C. Fefferman and E. Stein, H p spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
  7. [FJW] M. Frazier, B. Jawerth and G. Weiss, Littlewood-Paley Theory and the Study of Function Spaces, CBMS Regional Conf. Ser. 79, Amer. Math. Soc., 1991. Zbl0757.42006
  8. [H] Y.-S. Han, Triebel-Lizorkin spaces on spaces of homogeneous type, Studia Math. 108 (1994), 247-273. Zbl0822.46033
  9. [MS] R. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, Adv. in Math. 33 (1979), 271-309. Zbl0431.46019
  10. [M] A. Miyachi, On some Fourier multipliers for H p ( ℝ ) , J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), 157-179. Zbl0433.42019
  11. [S] C. E. Shannon, Communication in the presence of noise, Proc. IRE 37 (1949), 10-21. 
  12. [Su] Q. Sun, Sequence spaces and stability of integer translates, Z. Anal. Anwendungen 12 (1993), 567-584. Zbl0801.46006
  13. [U] A. Uchiyama, A maximal function characterization of H p on the spaces of homogeneous type, Trans. Amer. Math. Soc. 262 (1980), 579-592. Zbl0503.46020

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