Bounded mean oscillation with Orlicz norms and duality of Hardy spaces

Bounded Mean Oscillation with Orlicz Norms and Duality of Hardy Spaces

then it is still true that ƒ E BMO and (1) holds with A < CA'. In fact, a proof similar to that of [2] shows that (1)' implies (2). If the constant 1/2 in (1)' is replaced by a larger number, the result is no longer true. Let us now assume that the numbers A and A' in (1) resp. (1)' are not uniform but depend on x (but not on Q containing x). We define Mf(x) resp. MQ/(X) as the infîmum of such ...

Analytic Norms in Orlicz Spaces

It is shown that an Orlicz sequence space hM admits an equivalent analytic renorming if and only if it is either isomorphic to l2n or isomorphically polyhedral. As a consequence, we show that there exists a separable Banach space admitting an equivalent C∞-Fréchet norm, but no equivalent analytic norm. In this note, we denote by hM as usual the subspace of an Orlicz sequence space lM generated ...

Orlicz-Hardy Spaces Associated with Operators Satisfying Davies-Gaffney Estimates

Let X be a metric space with doubling measure, L be a nonnegative selfadjoint operator in L2(X ) satisfying the Davies-Gaffney estimate, ω be a concave function on (0,∞) of strictly lower type pω ∈ (0, 1] and ρ(t) = t/ω(t) for all t ∈ (0,∞). The authors introduce the Orlicz-Hardy space Hω,L(X ) via the Lusin area function associated to the heat semigroup, and the BMO-type space BMOρ,L(X ). The ...

New Orlicz-Hardy Spaces Associated with Divergence Form Elliptic Operators

Let L be the divergence form elliptic operator with complex bounded mea-surable coefficients, ω the positive concave function on (0,∞) of strictly critical lowertype pω ∈ (0, 1] and ρ(t) = t/ω(t) for t ∈ (0,∞). In this paper, the authorsstudy the Orlicz-Hardy spaceHω,L(R) and its dual spaceBMOρ,L∗(R), where L∗denotes the adjoint operator of L in L(R). Several characteriz...

Orlicz Spaces for Which the Hardy-littlewood Maximal Operator Is Bounded