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 -