Geodesic
Weighted variable Hardy spaces associated with operators satisfying Davies-Gaffney estimates
Problemy analiza, Tome 11 (2022) no. 3, pp. 66-90

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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 $L^2(\mathbb{R}^n)$.
Keywords: weighted Hardy spaces, variable exponent, Davies-Gaffney estimates, molecular decomposition, maximal function, dual space. 
@article{PA_2022_11_3_a5,
     author = {B. Laadjal and K. Saibi and O. Melkemi and Z. Mokhtari},
     title = {Weighted variable {Hardy} spaces associated with operators satisfying {Davies-Gaffney} estimates},
     journal = {Problemy analiza},
     pages = {66--90},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PA_2022_11_3_a5/}
}
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B. Laadjal; K. Saibi; O. Melkemi; Z. Mokhtari. Weighted variable Hardy spaces associated with operators satisfying Davies-Gaffney estimates. Problemy analiza, Tome 11 (2022) no. 3, pp. 66-90. http://geodesic.mathdoc.fr/item/PA_2022_11_3_a5/