English

On pointwise ergodic theorems for infinite measure

Functional Analysis 2016-09-21 v2

Abstract

For a Dunford-Schwartz operator in the LpL^p-space, 1p<1\leq p< \infty , of an arbitrary measure space, we prove pointwise convergence of the conventional and Besicovitch weighted ergodic averages. Pointwise convergence of various types of ergodic averages in fully symmetric spaces of measurable functions with non-trivial Boyd indices is studied. In particular, it is shown that for such spaces Bourgain's Return Times theorem is valid.

Keywords

Cite

@article{arxiv.1509.05938,
  title  = {On pointwise ergodic theorems for infinite measure},
  author = {Vladimir Chilin and Dogan Comez and Semyon Litvinov},
  journal= {arXiv preprint arXiv:1509.05938},
  year   = {2016}
}

Comments

This paper has been withdrawn by the author due to a crucial error in the last section

R2 v1 2026-06-22T11:00:43.022Z