Sharp bound for the ergodic maximal operator associated to Cesaro bounded operators

CABRAL, ADRIÁN; MARTÍN-REYES, FRANCISCO J.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2018 vol. 462 p. 648 - 664

0022-247X

We consider positive invertible Lamperti operators Tf(x)=h(x)Phi f(x) such that Phi has no periodic part. Let {A_{n,T}} be the sequence of averages of T and M_T the ergodic maximal operator. It is obvious that if M_T is bounded on some L^p, 1