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Commutators, Little Bmo And Weak Factorization, Xuan Thinh Duong, Ji Li, Brett D. Wick, Dongyong Yang
Commutators, Little Bmo And Weak Factorization, Xuan Thinh Duong, Ji Li, Brett D. Wick, Dongyong Yang
Mathematics Faculty Publications
In this paper, we provide a direct and constructive proof of weak factorization of h1 (ℝ×ℝ) (the predual of little BMO space bmo(ℝ×ℝ) studied by Cotlar-Sadosky and Ferguson-Sadosky), i.e., for every f Є h1 (ℝ×ℝ) there exist sequences {αkj} Є l and functions gjk, hkj Є L2 (ℝ2 ) such that [Equation Unavailable] in the sense of h1 (ℝ×ℝ), where H1 and H2 are the Hilbert transforms on the first and second variable, respectively. Moreover, the norm ║fh1║(ℝ×ℝ) is given in terms of ║gjk║ L2(ℝ2) and ║hkj║ L2(ℝ2). By duality, this directly implies a lower bound on the norm of …