On relations between operators on R^{N}, T^{N} and Z^{N}
Auscher, P. ; Carro, M.
Studia Mathematica, Tome 103 (1992), p. 165-182 / Harvested from The Polish Digital Mathematics Library
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We study different discrete versions of maximal operators and g-functions arising from a convolution operator on R. This allows us, in particular, to complete connections with the results of de Leeuw [L] and Kenig and Tomas [KT] in the setting of the groups R^{N}, T^{N} and Z^{N}.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:215899 
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     year = {1992},
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Auscher, P.; Carro, M. On relations between operators on R^{N}, T^{N} and Z^{N}. Studia Mathematica, Tome 103 (1992) pp. 165-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv101i2p165bwm/

[00000] [A] I. Assani, The Wiener-Wintner property for the Helical Transform of the shift on [0,1]^Z, preprint. | Zbl 0784.58036

[00001] [AP] I. Assani and K. Petersen, The helical transform as a connection between ergodic theory and harmonic analysis, Trans. Amer. Math. Soc., to appear. | Zbl 0768.47001

[00002] [B] R. P. Boas, Entire Functions, Academic Press, 1954. | Zbl 0058.30201

[00003] [Bo] J. Bourgain, Pointwise ergodic theorems for arithmetic sets, IHES Publ. Math. 69 (1989), 5-45.

[00004] [CP] J. Campbell and K. Petersen, The spectral measure and Hilbert transform of a measure-preserving transformation, Trans. Amer. Math. Soc. 313 (1989), 121-129. | Zbl 0675.28010

[00005] [C] L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135-157. | Zbl 0144.06402

[00006] [CW] R. Coifman and G. Weiss, Transference methods in analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., 1977.

[00007] [FS] R. Fefferman and F. Soria, The space Weak-H¹, Studia Math. 85 (1987), 1-16.

[00008] [HL] G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81-116. | Zbl 56.0264.02

[00009] [H] R. Hunt, On the convergence of Fourier series, in: Orthogonal Expansions and their Continuous Analogues, Proc. Conf. Edwardsville 1967, Southern Illinois Univ. Press, Carbondale, Ill., 1968, 235-255.

[00010] [KT] C. Kenig and P. Thomas, Maximal operators defined by Fourier multipliers, Studia Math. 68 (1980), 79-83. | Zbl 0442.42013

[00011] [L] K. de Leeuw, On L_p multipliers, Ann. of Math. 81 (1965), 364-379. | Zbl 0171.11803

[00012] [NRW1] A. Nagel, N. Rivière and S. Wainger, A maximal function associated to the curve (t,t²), Proc. Nat. Acad. Sci. U.S.A. 73 (5) (1976), 1416-1417. | Zbl 0325.43009

[00013] [NRW2] A. Nagel, On Hilbert transforms along curves. II, Amer. J. Math. 98 (2) (1976), 395-403.

[00014] [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. | Zbl 0207.13501

[00015] [SW] E. M. Stein and G. Weiss, Introduction to, Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.