Variable Hardy–Lorentz spaces associated to operators satisfying Davies–Gaffney estimates

Abstract

Let L be a one-to-one operator of type w with w∈[0,π/2), which satisfies the Davies–Gaffney estimates and has a bounded holomorphic calculus, and let p(⋅) be a measurable function on Rn with 0<p−:=essinf x∈Rnp(x)≤esssup x∈Rnp(x)=:p+<∞. Under the assumption that p(⋅) satisfies the global log-Holder condition, we introduce the variable Hardy–Lorentz space HLp(⋅),q(Rn) for 0<q<∞ and construct its molecular decomposition. Furthermore, we investigate the dual spaces of the variable Hardy–Lorentz space HLp(⋅),q(Rn) with 0<p−≤p+≤1 and 0<q<∞. These results are new even when p(⋅) is a constant.