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Boundedness of multilinear commutators of generalized fractional integrals
Author(s) -
Mo Huixia,
Lu Shanzhen
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510681
Subject(s) - mathematics , multilinear map , commutator , semigroup , generator (circuit theory) , kernel (algebra) , combinatorics , pure mathematics , algebra over a field , physics , power (physics) , lie conformal algebra , quantum mechanics
Let L be the infinitesimal generator of an analytic semigroup on L 2 (ℝ n ) with Gaussian kernel bound, and let L – α /2 be the fractional integral of L for 0 < α < n . Suppose that b = ( b 1 , b 2 , …, b m ) is a finite family of locally integral functions, then the multilinear commutator generated by b and L – α /2 is defined by L – α /2 b f = [ b m , …, [ b 2 , [ b 1 , L – α /2 ]], …, ] f , where m ∈ ℤ + . When b 1 , b 2 , …, b m ∈ BMO or b j ∈ Λ β j(0 < β j < 1) for 1 ≤ j ≤ m , the authors study the boundedness of L – α /2 b . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)