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.
@article{bwmeta1.element.bwnjournal-article-smv137i2p195bwm,
author = {Roger Jones},
title = {An exponential estimate for convolution powers},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {195-202},
zbl = {0959.28012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv137i2p195bwm}
}
Jones, Roger. An exponential estimate for convolution powers. Studia Mathematica, Tome 133 (1999) pp. 195-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv137i2p195bwm/
[00000] [1] A. Bellow and A. P. Calderón, A weak type inequality for convolution products, to appear.
[00001] [2] A. Bellow, R. L. Jones and J. Rosenblatt, Almost everywhere convergence of convolution powers, Ergodic Theory Dynam. Systems 14 (1994) 415-432. | Zbl 0818.28005
[00002] [3] R. A. Hunt, An estimate of the conjugate function, Studia Math. 44 (1972), 371-377. | Zbl 0219.42011
[00003] [4] R. L. Jones, Ergodic theory and connections with analysis and probability, New York J. Math. 3A (1997), 31-67. | Zbl 0898.28005
[00004] [5] R. L. Jones, Inequalities for the ergodic maximal function, Studia Math. 60 (1977), 111-129. | Zbl 0349.47007
[00005] [6] R. L. Jones, R. Kaufman, J. Rosenblatt and M. Wierdl, Oscillation in ergodic theory, Ergodic Theory Dynam. Systems 18 (1998), 889-935. | Zbl 0924.28009
[00006] [7] R. L. Jones, I. Ostrovskii and J. Rosenblatt, Square functions in ergodic theory, ibid. 16 (1996), 267-305.
[00007] [8] K. Reinhold, Convolution powers in , Illinois J. Math. 37 (1993), 666-679. | Zbl 0791.28012
[00008] [9] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970. | Zbl 0207.13501