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WEAK HERZ-TYPE HARDY SPACES WITH VARIABLE EXPONENTS AND APPLICATIONS
Souad Ben Seghier Korean Mathematical Society 2023 대한수학회지 Vol.60 No.1
Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝ<sup>n</sup> → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.
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