TY - JOUR
T1 - Weak Type Inequalities for Ergodic Strong Maximal Operators
AU - Hagelstein, Paul
AU - Stokolos, Alexander
PY - 2010/1/1
Y1 - 2010/1/1
N2 - Fava's weak type L log L 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 ε LΦ(L)(ω) is constructed whose associated multiparameter ergodic averages fail to converge almost everywhere in the unrestricted sense.
AB - Fava's weak type L log L 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 ε LΦ(L)(ω) is constructed whose associated multiparameter ergodic averages fail to converge almost everywhere in the unrestricted sense.
KW - Multiparameter ergodic averages
KW - Multiparameter ergodic maximal operators
UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/190
UR - http://pub.acta.hu/acta/showCustomerArticle.action?id=13014&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=1994e113dc3683ac&style=
M3 - Article
SN - 0001-6969
VL - 76
JO - Acta Scientiarum Mathematicarum
JF - Acta Scientiarum Mathematicarum
ER -