Orlicz-Hardy spaces associated with operators

Let L be a linear operator in L-2 (R-n) and generate an analytic semigroup {e(-tL)}(t >= 0) with kernel satisfying an upper bound of Poisson type, whose decay is measured by theta(L) is an element of (0, infinity). Let omega on (0, infinity) be of upper type 1 and of critical lower type (p) over tilde (0)(omega) is an element of (n/(n + theta(L)), 1] and rho(t) = t(-1)/omega(-1) (t(-1)) for t is an element of (0, infinity). We introduce the Orlicz-Hardy space H-omega,H- L(R-n) and the BMO-type space BMO rho, L(R-n) and establish the John-Nirenberg inequality for BMO rho, L(R-n) functions and the duality relation between H-omega,H- L(R-n) and BMO rho, L* (R-n), where L* denotes the adjoint operator of L in L-2(R-n). Using this duality relation, we further obtain the rho-Carleson measure characterization of BMO rho, L* (R-n) and the molecular characterization of H-omega,H- L(R-n); the latter is used to establish the boundedness of the generalized fractional operator L-rho(-gamma) from H-omega,H- L(R-n) to H-L(1) (R-n) or L-q (R-n) with certain q > 1, where H-L(1) (R-n) is the Hardy space introduced by Auscher, Duong and McIntosh. These results generalize the existing results by taking omega(t) - t(p) for t is an element of (0, infinity) and p is an element of (n/(n + theta(L)), 1].