Discrete Hardy spaces

• Autorzy: Santiago Boza , María J. Carro
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hardy spaces; discrete Hilbert transform; maximal operators

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 129
• Numer: 1
• Strony: 31-50

Daty

wydano

1998

otrzymano

1996-11-12

poprawiono

1997-10-27

Twórcy

autor

Santiago Boza

• Departament de Matemàtica, Aplicada i Telemàtic, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain.

autor

María J. Carro

• Departament de Matemàtica, Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain

Bibliografia

• [AC] P. Auscher and M. J. Carro, On relations between operators on $ℝ^N$, $𝕋^N$ and $ℤ^N$, Studia Math. 101 (1992), 165-182.
• [B] R. P. Boas, Entire Functions, Academic Press, 1954.
• [C] R. Coifman, A real-variable characterization of $H^p$, Studia Math. 51 (1974), 269-274.
• [CW] R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
• [E] C. M. Eoff, The discrete nature of the Paley-Wiener spaces, Proc. Amer. Math. Soc. 123 (1995), 505-512.
• [FS] C. Fefferman and E. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-193.
• [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.
• [H] Y.-S. Han, Triebel-Lizorkin spaces on spaces of homogeneous type, Studia Math. 108 (1994), 247-273.
• [MS] R. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, Adv. in Math. 33 (1979), 271-309.
• [M] A. Miyachi, On some Fourier multipliers for $H^p(ℝ)$, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), 157-179.
• [S] C. E. Shannon, Communication in the presence of noise, Proc. IRE 37 (1949), 10-21.
• [Su] Q. Sun, Sequence spaces and stability of integer translates, Z. Anal. Anwendungen 12 (1993), 567-584.
• [U] A. Uchiyama, A maximal function characterization of $H^p$ on the spaces of homogeneous type, Trans. Amer. Math. Soc. 262 (1980), 579-592.