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JOURNALS // Problemy Analiza — Issues of Analysis // Archive

Probl. Anal. Issues Anal., 2022 Volume 11(29), Issue 3, Pages 66–90 (Mi pa361)

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

B. Laadjala, K. Saibib, O. Melkemic, Z. Mokhtaric

a Laboratory of applied mathematics, University of Biskra, Biskra 07000, Algeria
b Department of mathematics, Zhejiang Normal University, Jinhua, China
c Laboratory of partial differential equations and applications, University of Batna 2, Batna 05000, Algeria

Abstract: 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.

UDC: 517.98, 512.642

MSC: 42B35

Received: 27.11.2021
Revised: 10.07.2022
Accepted: 13.07.2022

DOI: 10.15393/j3.art.2022.11130



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