Weak Type Inequality for the Square Function of a Nonnegative Submartingale

@article{AdamOsękowski2009,
abstract = {Let f be a nonnegative submartingale and S(f) denote its square function. We show that for any λ > 0, $λℙ(S(f) ≥ λ) ≤ π/2 ∥f∥₁$, and the constant π/2 is the best possible. The inequality is strict provided ∥f∥₁ ≠ 0.},
author = {Adam Osękowski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {submartingale; square function; weak type inequality},
language = {eng},
number = {1},
pages = {81-89},
title = {Weak Type Inequality for the Square Function of a Nonnegative Submartingale},
url = {http://eudml.org/doc/281209},
volume = {57},
year = {2009},
}

TY - JOUR
AU - Adam Osękowski
TI - Weak Type Inequality for the Square Function of a Nonnegative Submartingale
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2009
VL - 57
IS - 1
SP - 81
EP - 89
AB - Let f be a nonnegative submartingale and S(f) denote its square function. We show that for any λ > 0, $λℙ(S(f) ≥ λ) ≤ π/2 ∥f∥₁$, and the constant π/2 is the best possible. The inequality is strict provided ∥f∥₁ ≠ 0.
LA - eng
KW - submartingale; square function; weak type inequality
UR - http://eudml.org/doc/281209
ER -