Sharp Ratio Inequalities for a Conditionally Symmetric Martingale
Adam Osękowski (2010)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
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 such that . 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 such that . 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...