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

100%

Kikuchi M.

Colloquium Mathematicum

2013

tom 132

nr 1

13-26

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.

Some remarks on ratio inequalities for continuous martingales

38%

Kazamaki N., Kikuchi M.

Studia Mathematica

1989

tom 94

nr 1

97-102

Improved ratio inequalities for martingales

32%

Kikuchi M.

Studia Mathematica

1991

tom 99

nr 2

109-113

Ograniczanie wyników

2 Studia Mathematica

1 Colloquium Mathematicum

3 Kikuchi M.

1 Kazamaki N.

1 2013

1 1991

1 1989

Wyniki wyszukiwania

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

Some remarks on ratio inequalities for continuous martingales

Improved ratio inequalities for martingales