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Herz-type Hardy spaces with variable exponents associated with operators satisfying Davies–Gaffney estimates

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Abstract

Let L be a one-to-one operator of type w, with \(w\in [0,\pi /2]\), satisfying the Davies–Gaffney estimates. For \(\alpha \in (0,\infty )\) and \(p\in (0,\infty )\) and under the condition that \(q(\cdot ): {{{\mathbb {R}}}}^{n}\longrightarrow [1,\infty )\) satisfies the globally log-Hölder continuity condition, we introduce the Herz-type Hardy space with variable exponents associated to L and establish its molecular decomposition. The atomic characterization and maximal function characterizations of the space are proved under the assumption that L is a non-negative self-adjoint operator on \(L^{2}({{{\mathbb {R}}}}^{n})\) whose heat kernels satisfy the Gaussian upper bound estimates. All the results are new even for the constant case.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Souad Ben Seghier & Khedoudj Saibi

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  1. Souad Ben Seghier
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  2. Khedoudj Saibi
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Correspondence to Khedoudj Saibi.

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Communicated by S Thangavelu.

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Seghier, S.B., Saibi, K. Herz-type Hardy spaces with variable exponents associated with operators satisfying Davies–Gaffney estimates. Proc Math Sci 132, 19 (2022). https://doi.org/10.1007/s12044-022-00659-6

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  • DOI: https://doi.org/10.1007/s12044-022-00659-6

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