New Orlicz-Hardy spaces associated with divergence form elliptic operators

Let L be the divergence form elliptic operator with complex bounded measurable coefficients, omega the positive concave function on (0, infinity) of strictly critical lower type p(omega) is an element of (0, 1] and rho(t) = t(-1)/omega(-1)(t(-1)) for t is an element of (0, infinity). In this paper, the authors study the Orlicz-Hardy space H-omega,H-L(R-n) and its dual space BMO rho,L*(R-n), where L* denotes. the adjoint operator of L in L-2(R-n). Several characterizations of H-omega,H-L(R-n), including the molecular characterization, the Lusin-area function characterization and the maximal function characterization, are established. The rho-Carleson measure characterization and the John-Nirenberg inequality for the space BMO rho,L(R-n) are also given. As applications, the authors show that the Riesz transform del L-1/2 and the Littlewood-Paley g-function g(L) map H-omega,H-L(R-n) continuously into L(omega). The authors further show that the Riesz transform del L-1/2 maps H-omega,H-L(R-n) into the classical Orlicz-Hardy space H-omega(R-n) for p(omega) is an element of (n/n+1, 1] and the corresponding fractional integral L-gamma for certain gamma > 0 maps H-omega,H-L(R-n) continuously into H-(omega) over tilde ,H-L(R-n), where (omega) over tilde is determined by omega and gamma, and satisfies the same properly as omega. All these results are new even when omega(t) = t(p) for all t is an element of (0, infinity) and p is an element of (0, 1). (C) 2009 Elsevier Inc. All rights reserved.