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

P. Auscher; M. Carro

Studia Mathematica (1992)

  • Volume: 101, Issue: 2, page 165-182
  • ISSN: 0039-3223

Abstract

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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}.

How to cite

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Auscher, P., and Carro, M.. "On relations between operators on R^{N}, T^{N} and Z^{N}." Studia Mathematica 101.2 (1992): 165-182. <http://eudml.org/doc/215899>.

@article{Auscher1992,
abstract = {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\}.},
author = {Auscher, P., Carro, M.},
journal = {Studia Mathematica},
keywords = {maximal operators; -functions; convolution operator},
language = {eng},
number = {2},
pages = {165-182},
title = {On relations between operators on R^\{N\}, T^\{N\} and Z^\{N\}},
url = {http://eudml.org/doc/215899},
volume = {101},
year = {1992},
}

TY - JOUR
AU - Auscher, P.
AU - Carro, M.
TI - On relations between operators on R^{N}, T^{N} and Z^{N}
JO - Studia Mathematica
PY - 1992
VL - 101
IS - 2
SP - 165
EP - 182
AB - 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}.
LA - eng
KW - maximal operators; -functions; convolution operator
UR - http://eudml.org/doc/215899
ER -

References

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  10. [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. 
  11. [KT] C. Kenig and P. Thomas, Maximal operators defined by Fourier multipliers, Studia Math. 68 (1980), 79-83. Zbl0442.42013
  12. [L] K. de Leeuw, On L_p multipliers, Ann. of Math. 81 (1965), 364-379. Zbl0171.11803
  13. [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. Zbl0325.43009
  14. [NRW2] A. Nagel, On Hilbert transforms along curves. II, Amer. J. Math. 98 (2) (1976), 395-403. 
  15. [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. Zbl0207.13501
  16. [SW] E. M. Stein and G. Weiss, Introduction to, Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971. 

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