## Abstract

Let U _{1},...,U _{d} be a non-periodic collection of commuting measure pre- serving transformations on a probability space ΩΣμ): Also let Γ be a nonempty subset of Z ^{d} _{+} and B the associated collection of rectangular parallelepipeds in R ^{d} with sides par- allel to the axes and dimensions of the form n _{1} x...x n _{d} with (n _{1},...,n _{d}) ∈ Γ. The associated multiparameter geometric and ergodic maximal operators M _{B} and M _{Γ} are deFIned respectively on L ^{1}(R ^{d}) and L ^{1}(Ω) by {equation presented} Given a Young function φ, it is shown that M _{B} satisfies the weak type estimate {equation presented} for a pair of positive constants CB, cB if and only if MΓ satisfies a corresponding weak type estimate {equation presented} for a pair of positive constants CΓ,cΓ. Applications of this transference principle regarding the a.e. convergence of multiparameter ergodic averages associated to rare bases are given.

Original language | American English |
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Journal | Fundamenta Mathematicae |

Volume | 218 |

DOIs | |

State | Published - Jan 1 2012 |

## Keywords

- Multiparameter geometric and ergodic maximal operator

## DC Disciplines

- Education
- Mathematics