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Musielak–Orlicz Hardy Spaces Associated with Divergence Form Elliptic Operators Without Weight Assumptions

Published online by Cambridge University Press:  11 January 2016

Tri Dung Tran
Tri Dung Tran*
Affiliation:
Department of Mathematics, University of Pedagogy, Ho Chi Minh city, Vietnamtridung.tran@mq.edu.au, tridungsp@gmail.com
*
Department of Mathematics, Macquarie University, NSW 2109, Australia
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Abstract

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Let L be a divergence form elliptic operator with complex bounded measurable coefficients, let ω be a positive Musielak-Orlicz function on (0, ∞) of uniformly strictly critical lower-type pω ∈ (0, 1], and let ρ(x,t) = t−1/ω−1 (x,t−1) for x ∈ ℝn, t ∊ (0, ∞). In this paper, we study the Musielak-Orlicz Hardy space Hω,L(ℝn) and its dual space BMOρ,L* (ℝ n), where L* denotes the adjoint operator of L in L2 (ℝ n). The ρ-Carleson measure characterization and the John-Nirenberg inequality for the space BMOρ,L (ℝn) are also established. Finally, as applications, we show that the Riesz transform ∇L−1/2 and the Littlewood–Paley g-function gL map Hω,L(ℝn) continuously into L(ω).

Keywords

42B2035B6535K0542B2547B3858J35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 216 , 2014 , pp. 71 - 110
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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