# An exponential estimate for convolution powers

Studia Mathematica (1999)

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

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topJones, 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

top- [1] A. Bellow and A. P. Calderón, A weak type inequality for convolution products, to appear.
- [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] R. A. Hunt, An estimate of the conjugate function, Studia Math. 44 (1972), 371-377. Zbl0219.42011
- [4] R. L. Jones, Ergodic theory and connections with analysis and probability, New York J. Math. 3A (1997), 31-67. Zbl0898.28005
- [5] R. L. Jones, Inequalities for the ergodic maximal function, Studia Math. 60 (1977), 111-129. Zbl0349.47007
- [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] R. L. Jones, I. Ostrovskii and J. Rosenblatt, Square functions in ergodic theory, ibid. 16 (1996), 267-305.
- [8] K. Reinhold, Convolution powers in ${L}^{1}$, Illinois J. Math. 37 (1993), 666-679. Zbl0791.28012
- [9] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0207.13501

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