## Abstract

Let L be a divergence form elliptic operator with complexbounded measurable coefficients, let ω be a positive Musielak-Orlicz functionon (0,∞) of uniformly strictly critical lower-type p
_{ω} ε (0, 1], and let ρ(x, t) =t
^{-1}/ω-1(x, t
^{-1}) for x ε R
^{n}, t ε (0,∞). In this paper, we study the Musielak-Orlicz Hardy space Hω,L(R
^{n}) and its dual space BMOρ,L* (R
^{n}), where L*denotes the adjoint operator of L in L
^{2}(R
^{n}). The ρ-Carleson measure characterizationand the John-Nirenberg inequality for the space BMOρ,L(R
^{n}) are also established. Finally, as applications, we show that the Riesz transform∇L-
^{1/2} and the Littlewood-Paley g-function gL map H
_{ω,L}(R
^{n}) continuouslyinto L(ω).

Original language | English |
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Pages (from-to) | 71-110 |

Number of pages | 40 |

Journal | Nagoya Mathematical Journal |

Volume | 216 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 2014 |