Atomic Decompositions of Hardy Spaces with Variable Exponents and its Application to Bounded Linear Operators

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Characterizations of variable exponent Hardy spaces via Riesz transforms (2015, background): “Later, in [19], Sawano extended the atomic characterization of the space Hp(·)(Rn) in [14], which also improves the corresponding result in [14], and gave out more applications including the boundedness of several operators.”
Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents (2014, methodology): “For a systematic research about the variable exponent Lebesgue space, we refer the reader to [8, 13] Recently, Nakai and Sawano [32] extended the theory of variable Lebesgue spaces via studying the Hardy spaces with variable exponents on R, and Sawano in [35] further gave more applications of these ”
New Hardy Spaces of Musielak–Orlicz Type and Boundedness of Sublinear Operators (2011, background): “Recently, new Hardy spaces of Musielak–Orlicz type have developed in many directions (see [11,47,50,56,57]), some their characterizations and applications were also established and studied in [11,27,38,50].”
Variable Hardy–Lorentz spaces Hp(·),q(Rn) (2018, result): “Sawano [49] further extended the atomic characterization of Hp(⋅)(Rn) and improved the corresponding results in [44].”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, background): “[203] Suppose either (i) or (ii) holds; (i) 0 < p− ≤ p+ < q ≤ ∞ and p+ ≥ 1; (ii) 0 < p− ≤ p+ < 1 ≤ q ≤ ∞.”