ArticleOriginal scientific text
Title
An exponential estimate for convolution powers
Authors 1
Affiliations
- Department of Mathematics, DePaul University, 2219 N. Kenmore, Chicago, IL 60614, U.S.A.
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.
Keywords
maximal functions, exponential estimates, convolution powers
Bibliography
- A. Bellow and A. P. Calderón, A weak type inequality for convolution products, to appear.
- A. Bellow, R. L. Jones and J. Rosenblatt, Almost everywhere convergence of convolution powers, Ergodic Theory Dynam. Systems 14 (1994) 415-432.
- R. A. Hunt, An estimate of the conjugate function, Studia Math. 44 (1972), 371-377.
- R. L. Jones, Ergodic theory and connections with analysis and probability, New York J. Math. 3A (1997), 31-67.
- R. L. Jones, Inequalities for the ergodic maximal function, Studia Math. 60 (1977), 111-129.
- R. L. Jones, R. Kaufman, J. Rosenblatt and M. Wierdl, Oscillation in ergodic theory, Ergodic Theory Dynam. Systems 18 (1998), 889-935.
- R. L. Jones, I. Ostrovskii and J. Rosenblatt, Square functions in ergodic theory, ibid. 16 (1996), 267-305.
- K. Reinhold, Convolution powers in
, Illinois J. Math. 37 (1993), 666-679. - E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.