On Nörlund summation and ergodic theory, with applications to power series of Hilbert contractions

We show that if a = (an)n∈N is a good weight for the dominated weighted ergodic theorem in Lp, p > 1, then the Nörlund matrix Na = {ai−j / Ai}0≤j≤i, Ai = ∑ik=0|ak|, is bounded on ℓp(N). We study the regularity (convergence in norm and almost everywhere) of operators in ergodic theory: power series of Hilbert contractions and power series ∑n∈N an Pn f of L2-contractions, and establish similar close relations to the Nörlund operator associated to the modulus coefficient sequence (|an|)n∈N.

---

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).