John–Nirenberg inequality and atomic decomposition for noncommutative martingales
Copyright policy )John–Nirenberg inequality and atomic decomposition for noncommutative martingales
In this paper, we study the John-Nirenberg inequality for BMO and the atomic decomposition for H1 of noncommutative martingales. We first establish a crude version of the column (resp. row) John-Nirenberg inequality for all 0 < p < \infty. By an extreme point property of Lp -space for 0 < p \leq 1, we then obtain a fine version of this in equality. The latter corresponds exactly to the classical John-Nirenberg inequality and enables us to obtain an exponential integrability inequality like in the classical case. These results extend and improve Junge and Musat's John-Nirenberg inequality. By duality, we obtain the corresponding q-atomic decomposition for different Hardy spaces H1 for all 1
- Wayne State College United States
- UNIVERSITE DE BESANCON [FRANCHE-COMTE] France
- Wayne State University United States
- University of Illinois at Urbana-Champaign United States
- UNIVERSITE MARIE ET LOUIS PASTEUR France
John, Probability (math.PR), Mathematics - Operator Algebras, Noncommutative probability and statistics, noncommutative \(L_{p}\)-spaces, Noncommutative function spaces, noncommutative martingales, Functional Analysis (math.FA), Noncommutative martingales, Mathematics - Functional Analysis, Mathematics - Classical Analysis and ODEs, Noncommutative Lp-spaces, Classical Analysis and ODEs (math.CA), FOS: Mathematics, John–Nirenberg inequality, Atomic decomposition, Hardy spaces and BMO spaces, Nirenberg inequality, Operator Algebras (math.OA), Analysis, Mathematics - Probability, atomic decomposition
John, Probability (math.PR), Mathematics - Operator Algebras, Noncommutative probability and statistics, noncommutative \(L_{p}\)-spaces, Noncommutative function spaces, noncommutative martingales, Functional Analysis (math.FA), Noncommutative martingales, Mathematics - Functional Analysis, Mathematics - Classical Analysis and ODEs, Noncommutative Lp-spaces, Classical Analysis and ODEs (math.CA), FOS: Mathematics, John–Nirenberg inequality, Atomic decomposition, Hardy spaces and BMO spaces, Nirenberg inequality, Operator Algebras (math.OA), Analysis, Mathematics - Probability, atomic decomposition
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