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

• Autorzy: Masato Kikuchi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 46N30: Applications in probability theory and statistics
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 60G42: Martingales with discrete parameter
• 60G46: Martingales and classical analysis

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 132
• Numer: 1
• Strony: 13-26

Daty

wydano

2013

Twórcy

autor

Masato Kikuchi

• Department of Mathematics, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan

Identyfikatory

DOI

10.4064/cm132-1-2