Weighted variable Hardy spaces associated with operators satisfying Davies-Gaffney estimates

B. Laadjal ; K. Saibi ; O. Melkemi ; Z. Mokhtari

Problemy analiza, Tome 11 (2022) no. 3, pp. 66-90.

Résumé

We introduce the weighted variable Hardy space $H^{p(\cdot)}_{L,w}(\mathbb{R}^n)$ 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 $H^{p(\cdot)}_{L,w}(\mathbb{R}^n)$ and we show that the new weighted variable bounded mean oscillation-type space $BMO^{p(\cdot),M}_{L^*,w}$ represents the dual space of $H^{p(\cdot)}_{L,w}(\mathbb{R}^n)$, where $L^*$ denotes the adjoint operator of $L$ on $L^2(\mathbb{R}^n)$.

Détail

Keywords: weighted Hardy spaces, variable exponent, Davies-Gaffney estimates, molecular decomposition, maximal function, dual space.

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