Pointwise convergence for subsequences of weighted averages

• Autorzy: Patrick LaVictoire
• Języki publikacji: EN

Abstrakty

EN

We prove that if μₙ are probability measures on ℤ such that μ̂ₙ converges to 0 uniformly on every compact subset of (0,1), then there exists a subsequence ${n_{k}}$ such that the weighted ergodic averages corresponding to $μ_{n_{k}}$ satisfy a pointwise ergodic theorem in L¹. We further discuss the relationship between Fourier decay and pointwise ergodic theorems for subsequences, considering in particular the averages along n² + ⌊ρ(n)⌋ for a slowly growing function ρ. Under some monotonicity assumptions, the rate of growth of ρ'(x) determines the existence of a "good" subsequence of these averages.

Kategorie tematyczne

• 37A30: Ergodic theorems, spectral theory, Markov operators
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 124
• Numer: 2
• Strony: 157-168

Daty

wydano

2011

Twórcy

autor

Patrick LaVictoire

• Department of Mathematics, University of Wisconsin at Madison, Madison, WI 53706-1388, U.S.A.

Identyfikatory

DOI

10.4064/cm124-2-2