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Complex Convexity and Vector‐Valued Littlewood–Paley Inequalities
Author(s) -
Blasco Oscar,
Pavlović Miroslav
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002479
Subject(s) - mathematics , convexity , mathematics subject classification , banach space , regular polygon , space (punctuation) , pure mathematics , combinatorics , convex function , poisson distribution , geometry , statistics , financial economics , economics , linguistics , philosophy
Let 2 ⩽ p > ∞, and let X be a complex Banach space. It is shown that X is p ‐uniformly PL‐convex if and only if there exists λ > 0 such that‖ f ‖H p ( X )⩾(‖ f ( 0 )‖ p + λ ∫ D( 1 −| z | 2 )p − 1‖f ′ ( z )‖ p d A ( z ) )1 / p, for all f ∈ H p ( X ). Applications to embeddings between vector‐valued BMOA spaces defined via Poisson integral or Carleson measures are provided. 2000 Mathematics Subject Classification 46B20, 46L52.