WEIGHTED VARIABLE HARDY SPACES ASSOCIATED WITH OPERATORS SATISFYING DAVIES-GAFFNEY ESTIMATES

Abstract

We introduce the weighted variable Hardy space 𝐻(^𝑝(·) _𝐿,𝑤) (ℝ^𝑛) associated with the operator 𝐿, which has a bounded holomorphic functional calculus and fulfills the Davies-Gaffney estimates. More precisely, we establish the molecular characterization of 𝐻(^𝑝(·) _𝐿,𝑤) (ℝ^𝑛) and we show that the new weighted variable bounded mean oscillation-type space 𝐵𝑀𝑂(^𝑝(·),𝑀 _𝐿*,𝑤) represents the dual space of 𝐻(^𝑝(·) _𝐿,𝑤) (ℝ^𝑛), where 𝐿* denotes the adjoint operator of 𝐿 on 𝐿^2(ℝ^𝑛).

Keywords

• weighted hardy spaces
• variable exponent
• daviesgaffney estimates
• molecular decomposition
• maximal function
• dual space