Pointwise limit theorem for a class of unbounded operators in ${}^r$-spaces

Ryszard Jajte. "Pointwise limit theorem for a class of unbounded operators in $^{r}$-spaces." Studia Mathematica 179.1 (2007): 49-61. <http://eudml.org/doc/284832>.

@article{RyszardJajte2007,
abstract = {We distinguish a class of unbounded operators in $^\{r\}$, r ≥ 1, related to the self-adjoint operators in ². For these operators we prove a kind of individual ergodic theorem, replacing the classical Cesàro averages by Borel summability. The result is equivalent to a version of Gaposhkin’s criterion for the a.e. convergence of operators. In the proof, the theory of martingales and interpolation in $^\{r\}$-spaces are applied.},
author = {Ryszard Jajte},
journal = {Studia Mathematica},
keywords = {individual ergodic theorem; martingale transform; square function; Burkholder interpolation inequality in -spaces; Borel summability},
language = {eng},
number = {1},
pages = {49-61},
title = {Pointwise limit theorem for a class of unbounded operators in $^\{r\}$-spaces},
url = {http://eudml.org/doc/284832},
volume = {179},
year = {2007},
}

TY - JOUR
AU - Ryszard Jajte
TI - Pointwise limit theorem for a class of unbounded operators in $^{r}$-spaces
JO - Studia Mathematica
PY - 2007
VL - 179
IS - 1
SP - 49
EP - 61
AB - We distinguish a class of unbounded operators in $^{r}$, r ≥ 1, related to the self-adjoint operators in ². For these operators we prove a kind of individual ergodic theorem, replacing the classical Cesàro averages by Borel summability. The result is equivalent to a version of Gaposhkin’s criterion for the a.e. convergence of operators. In the proof, the theory of martingales and interpolation in $^{r}$-spaces are applied.
LA - eng
KW - individual ergodic theorem; martingale transform; square function; Burkholder interpolation inequality in -spaces; Borel summability
UR - http://eudml.org/doc/284832
ER -