An \(L^1\) counting problem in ergodic theory

DOI10.1007/BF02791503zbMath1110.28013arXivmath/0307384OpenAlexW2112302453MaRDI QIDQ2565920

Idris Assani, Zoltán Buczolich, R. Daniel Mauldin

Publication date: 28 September 2005

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307384

zbMATH Keywords

maximal operatorreturn time theorem

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Dynamical aspects of measure-preserving transformations (37A05)

Related Items (10)

The return times property for the tail on logarithm-type spaces ⋮ Extrapolation on \(L^{p,\infty}({\mu})\) ⋮ Modulated \((C,\alpha)\)-ergodic theorems with non-integral orders for Dunford-Schwartz operators ⋮ Convergence of ergodic averages for many group rotations ⋮ Breaking the duality in the return times theorem ⋮ Endpoint estimates for Rubio de Francia operators ⋮ Divergent square averages ⋮ A counting problem in ergodic theory and extrapolation for one-sided weights ⋮ Boundedness of sparse and rough operators on weighted Lorentz spaces ⋮ Weighted weak-type \((1, 1)\) estimates via Rubio de Francia extrapolation

Cites Work

• Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
• Strong laws for weighted sums of independent identically distributed random variables
• Convergence of the \(p\)-series for stationary sequences
• Fully generic sequences and a multiple-term return-times theorem
• A weighted pointwise ergodic theorem
• A joinings proof of Bourgain's return time theorem
• Counting in Ergodic Theory
• On restricted weak type (1,1); the discrete case
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