A Note on the Burkholder-Rosenthal Inequality

Adam Osękowski. "A Note on the Burkholder-Rosenthal Inequality." Bulletin of the Polish Academy of Sciences. Mathematics 60.2 (2012): 177-185. <http://eudml.org/doc/281326>.

@article{AdamOsękowski2012,
abstract = {Let df be a Hilbert-space-valued martingale difference sequence. The paper is devoted to a new, elementary proof of the estimate $∥∑_\{k=0\}^\{∞\} df_k∥_p ≤ C_p \{∥(∑_\{k=0\}^\{∞\} (|df_k|²| ℱ_\{k-1\}))^\{1/2\}∥_p + ∥(∑_\{k=0\}^\{∞\} |df_k|^p)^\{1/p\}∥_p\},$ with $C_p = O(p/lnp)$ as p → ∞.},
author = {Adam Osękowski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
language = {eng},
number = {2},
pages = {177-185},
title = {A Note on the Burkholder-Rosenthal Inequality},
url = {http://eudml.org/doc/281326},
volume = {60},
year = {2012},
}

TY - JOUR
AU - Adam Osękowski
TI - A Note on the Burkholder-Rosenthal Inequality
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 2
SP - 177
EP - 185
AB - Let df be a Hilbert-space-valued martingale difference sequence. The paper is devoted to a new, elementary proof of the estimate $∥∑_{k=0}^{∞} df_k∥_p ≤ C_p {∥(∑_{k=0}^{∞} (|df_k|²| ℱ_{k-1}))^{1/2}∥_p + ∥(∑_{k=0}^{∞} |df_k|^p)^{1/p}∥_p},$ with $C_p = O(p/lnp)$ as p → ∞.
LA - eng
UR - http://eudml.org/doc/281326
ER -