Weak Type Inequality for the Square Function of a Nonnegative Submartingale
Adam Osękowski
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009), p. 81-89 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:281209 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-9,
     author = {Adam Os\k ekowski},
     title = {Weak Type Inequality for the Square Function of a Nonnegative Submartingale},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {57},
     year = {2009},
     pages = {81-89},
     zbl = {1173.60015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-9}
}

Adam Osękowski. Weak Type Inequality for the Square Function of a Nonnegative Submartingale. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 81-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-9/