Title

Weak Type Inequalities for Ergodic Strong Maximal Operators

Document Type

Article

Publication Date

2010

Publication Title

Acta Scientiarum Mathematicarum

ISSN

0001-6969

Abstract

Fava's weak type LlogL estimate for strong two-parameter ergodic maximal operators associated to pairs of commuting non-periodic measure-preserving transformations is shown to be sharp. Moreover, given a function ϕ on [0, ∞) that is positive, increasing, and o(log(x)) for x → ∞ as well as a pair of commuting invertible non-periodic measure-preserving transformations on a space Ω of finite measure, a function f∈Lϕ(L)(Ω) is constructed whose associated multiparameter ergodic averages fail to converge almost everywhere in the unrestricted sense.

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