On a relation between norms of the maximal function and the square function of a martingale

Masato Kikuchi. "On a relation between norms of the maximal function and the square function of a martingale." Colloquium Mathematicae 132.1 (2013): 13-26. <http://eudml.org/doc/286638>.

@article{MasatoKikuchi2013,
abstract = {Let Ω be a nonatomic probability space, let X be a Banach function space over Ω, and let ℳ be the collection of all martingales on Ω. For $f = (fₙ)_\{n∈ℤ₊\} ∈ ℳ $, let Mf and Sf denote the maximal function and the square function of f, respectively. We give some necessary and sufficient conditions for X to have the property that if f, g ∈ ℳ and $||Mg||_\{X\} ≤ ||Mf||_\{X\}$, then $||Sg||_\{X\} ≤ C||Sf||_\{X\}$, where C is a constant independent of f and g.},
author = {Masato Kikuchi},
journal = {Colloquium Mathematicae},
keywords = {martingale; Banach function space; maximal function; square function},
language = {eng},
number = {1},
pages = {13-26},
title = {On a relation between norms of the maximal function and the square function of a martingale},
url = {http://eudml.org/doc/286638},
volume = {132},
year = {2013},
}

TY - JOUR
AU - Masato Kikuchi
TI - On a relation between norms of the maximal function and the square function of a martingale
JO - Colloquium Mathematicae
PY - 2013
VL - 132
IS - 1
SP - 13
EP - 26
AB - Let Ω be a nonatomic probability space, let X be a Banach function space over Ω, and let ℳ be the collection of all martingales on Ω. For $f = (fₙ)_{n∈ℤ₊} ∈ ℳ $, let Mf and Sf denote the maximal function and the square function of f, respectively. We give some necessary and sufficient conditions for X to have the property that if f, g ∈ ℳ and $||Mg||_{X} ≤ ||Mf||_{X}$, then $||Sg||_{X} ≤ C||Sf||_{X}$, where C is a constant independent of f and g.
LA - eng
KW - martingale; Banach function space; maximal function; square function
UR - http://eudml.org/doc/286638
ER -