On relations between operators on R^{N}, T^{N} and Z^{N}

• Autorzy: P. Auscher , M. J. Carro
• Języki publikacji: EN

Abstrakty

EN

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}.

Kategorie tematyczne

• 42B15: Multipliers
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991-1992
• Tom: 101
• Numer: 2
• Strony: 165-182

Daty

wydano

1992

otrzymano

1990-10-30

Twórcy

autor

P. Auscher

• Department Of Mathematics, Washington University, Box 1146, St. Louis, Missouri 63130, U.S.A.

autor

M. J. Carro

• Departament de Matemátiques, Facultat de Ciences, Universitat Autónoma de Barcelona, 08193 Bellaterra (Barcelona), Spain

Bibliografia

• [A] I. Assani, The Wiener-Wintner property for the Helical Transform of the shift on [0,1]^Z, preprint.
• [AP] I. Assani and K. Petersen, The helical transform as a connection between ergodic theory and harmonic analysis, Trans. Amer. Math. Soc., to appear.
• [B] R. P. Boas, Entire Functions, Academic Press, 1954.
• [Bo] J. Bourgain, Pointwise ergodic theorems for arithmetic sets, IHES Publ. Math. 69 (1989), 5-45.
• [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.
• [C] L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135-157.
• [CW] R. Coifman and G. Weiss, Transference methods in analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., 1977.
• [FS] R. Fefferman and F. Soria, The space Weak-H¹, Studia Math. 85 (1987), 1-16.
• [HL] G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), 81-116.
• [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.
• [KT] C. Kenig and P. Thomas, Maximal operators defined by Fourier multipliers, Studia Math. 68 (1980), 79-83.
• [L] K. de Leeuw, On L_p multipliers, Ann. of Math. 81 (1965), 364-379.
• [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.
• [NRW2] A. Nagel, On Hilbert transforms along curves. II, Amer. J. Math. 98 (2) (1976), 395-403.
• [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
• [SW] E. M. Stein and G. Weiss, Introduction to, Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.