BMO Martingales

Ruilin Long

Chapter 4 in Martingale Spaces and Inequalities, 1993, pp 129-172 from Springer

Abstract: Abstract Let (Ω, F, μ, {F n }n≥0) be as defined in §2.1. The Banach spaces BMO a , 1 ≤ a ≤ ∞, are defined as follows B M O a = { f = ( f n ) n ⩾ 0 ∈ L u a : ‖ f ‖ B M O a = sup n ‖ E ( | f − f n − 1 | a | F n ) 1 a ‖ ∞ < ∞ } $$BM{O_a} = \left\{ {f = {{\left( {{f_n}} \right)}_{n \geqslant 0}} \in L_u^a:\left\| f \right\|BM{O_a} = \mathop {\sup }\limits_n {{\left\| {E{{\left( {{{\left| {f - {f_{n - 1}}} \right|}^a}\left| {{F_n}} \right.} \right)}^{\frac{1}{a}}}} \right\|}_\infty }

Keywords: Classical Case; Carleson Measure; Require Norm Estimate; Commutator Theory; Stop Time Argument (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1007/978-3-322-99266-6_4

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