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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
Аннотация:
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 $L^2(\mathbb{R}^n)$.
Ключевые слова:
weighted Hardy spaces, variable exponent, Davies-Gaffney estimates, molecular decomposition, maximal function, dual space.
Поступила в редакцию: 27.11.2021 Исправленный вариант: 10.07.2022 Принята в печать: 13.07.2022
Образец цитирования:
B. Laadjal, K. Saibi, O. Melkemi, Z. Mokhtari, “Weighted variable Hardy spaces associated with operators satisfying Davies-Gaffney estimates”, Пробл. анал. Issues Anal., 11(29):3 (2022), 66–90
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa361 https://www.mathnet.ru/rus/pa/v29/i3/p66
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