An exponential estimate for convolution powers

Roger Jones

Studia Mathematica (1999)

  • Volume: 137, Issue: 2, page 195-202
  • ISSN: 0039-3223

Abstract

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We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.

How to cite

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Jones, Roger. "An exponential estimate for convolution powers." Studia Mathematica 137.2 (1999): 195-202. <http://eudml.org/doc/216684>.

@article{Jones1999,
abstract = {We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.},
author = {Jones, Roger},
journal = {Studia Mathematica},
keywords = {maximal functions; exponential estimates; convolution powers; ergodic theorem; weighted averages},
language = {eng},
number = {2},
pages = {195-202},
title = {An exponential estimate for convolution powers},
url = {http://eudml.org/doc/216684},
volume = {137},
year = {1999},
}

TY - JOUR
AU - Jones, Roger
TI - An exponential estimate for convolution powers
JO - Studia Mathematica
PY - 1999
VL - 137
IS - 2
SP - 195
EP - 202
AB - We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.
LA - eng
KW - maximal functions; exponential estimates; convolution powers; ergodic theorem; weighted averages
UR - http://eudml.org/doc/216684
ER -

References

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  1. [1] A. Bellow and A. P. Calderón, A weak type inequality for convolution products, to appear. 
  2. [2] A. Bellow, R. L. Jones and J. Rosenblatt, Almost everywhere convergence of convolution powers, Ergodic Theory Dynam. Systems 14 (1994) 415-432. Zbl0818.28005
  3. [3] R. A. Hunt, An estimate of the conjugate function, Studia Math. 44 (1972), 371-377. Zbl0219.42011
  4. [4] R. L. Jones, Ergodic theory and connections with analysis and probability, New York J. Math. 3A (1997), 31-67. Zbl0898.28005
  5. [5] R. L. Jones, Inequalities for the ergodic maximal function, Studia Math. 60 (1977), 111-129. Zbl0349.47007
  6. [6] R. L. Jones, R. Kaufman, J. Rosenblatt and M. Wierdl, Oscillation in ergodic theory, Ergodic Theory Dynam. Systems 18 (1998), 889-935. Zbl0924.28009
  7. [7] R. L. Jones, I. Ostrovskii and J. Rosenblatt, Square functions in ergodic theory, ibid. 16 (1996), 267-305. 
  8. [8] K. Reinhold, Convolution powers in L 1 , Illinois J. Math. 37 (1993), 666-679. Zbl0791.28012
  9. [9] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0207.13501

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