ATOMIC DECOMPOSITION OF HARDY-MORREY SPACES WITH VARIABLE EXPONENTS

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Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood–Paley Characterizations and Real Interpolation (2019, unknown): “7 (see, for instance, [19, 38]).”
Martingale Hardy spaces with variable exponents (2014, unknown): “ ≤ ( X k∈Z µk χ{τ k<∞} kχ{τ k<∞}kp(·) p)1 p p(·) = A({µk},{ak},{τk}). Hence we canconclude thatkfkHs p(·) ≈kfkHs,at p(·) andtheproofiscomplete now. Remark 4.3. It is showed in Theorem 5.1 in [14] that, for the atomic decomposition of Hardy-Morrey spaces with variable exponents p(·) on Rn, the”