An exponential estimate for convolution powers

• Autorzy: Roger L. Jones
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

maximal functions; exponential estimates; convolution powers

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 137
• Numer: 2
• Strony: 195-202

Daty

wydano

1999

poprawiono

1999-01-18

poprawiono

1999-09-24

Twórcy

autor

Roger L. Jones

• Department of Mathematics, DePaul University, 2219 N. Kenmore, Chicago, IL 60614, U.S.A.

Bibliografia

• [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.
• [3] R. A. Hunt, An estimate of the conjugate function, Studia Math. 44 (1972), 371-377.
• [4] R. L. Jones, Ergodic theory and connections with analysis and probability, New York J. Math. 3A (1997), 31-67.
• [5] R. L. Jones, Inequalities for the ergodic maximal function, Studia Math. 60 (1977), 111-129.
• [6] R. L. Jones, R. Kaufman, J. Rosenblatt and M. Wierdl, Oscillation in ergodic theory, Ergodic Theory Dynam. Systems 18 (1998), 889-935.
• [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.
• [9] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.