Sharp Ratio Inequalities for a Conditionally Symmetric Martingale

Adam Osękowski. "Sharp Ratio Inequalities for a Conditionally Symmetric Martingale." Bulletin of the Polish Academy of Sciences. Mathematics 58.1 (2010): 65-77. <http://eudml.org/doc/281210>.

@article{AdamOsękowski2010,
abstract = {Let f be a conditionally symmetric martingale and let S(f) denote its square function. (i) For p,q > 0, we determine the best constants $C_\{p,q\}$ such that $sup_n (|fₙ|^p)/(1+Sₙ²(f))^q ≤ C_\{p,q\}$. Furthermore, the inequality extends to the case of Hilbert space valued f. (ii) For N = 1,2,... and q > 0, we determine the best constants $C^\{\prime \}_\{N,q\}$ such that $sup_n (fₙ^\{2N-1\})(1+Sₙ²(f))^q ≤ C^\{\prime \}_\{N,q\}$. These bounds are extended to sums of conditionally symmetric variables which are not necessarily integrable. In addition, we show that neither of the inequalities above holds if the conditional symmetry is not assumed.},
author = {Adam Osękowski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
language = {eng},
number = {1},
pages = {65-77},
title = {Sharp Ratio Inequalities for a Conditionally Symmetric Martingale},
url = {http://eudml.org/doc/281210},
volume = {58},
year = {2010},
}

TY - JOUR
AU - Adam Osękowski
TI - Sharp Ratio Inequalities for a Conditionally Symmetric Martingale
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2010
VL - 58
IS - 1
SP - 65
EP - 77
AB - Let f be a conditionally symmetric martingale and let S(f) denote its square function. (i) For p,q > 0, we determine the best constants $C_{p,q}$ such that $sup_n (|fₙ|^p)/(1+Sₙ²(f))^q ≤ C_{p,q}$. Furthermore, the inequality extends to the case of Hilbert space valued f. (ii) For N = 1,2,... and q > 0, we determine the best constants $C^{\prime }_{N,q}$ such that $sup_n (fₙ^{2N-1})(1+Sₙ²(f))^q ≤ C^{\prime }_{N,q}$. These bounds are extended to sums of conditionally symmetric variables which are not necessarily integrable. In addition, we show that neither of the inequalities above holds if the conditional symmetry is not assumed.
LA - eng
UR - http://eudml.org/doc/281210
ER -