Generalized weighted Morrey spaces and classical operators

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A Thought on Generalized Morrey Spaces (2018, background): “See [82, 78, 94] for the strong boundedness of the maximal operators, where the integral conditions is not assumed.”
The singular integral operator and its commutator on weighted Morrey spaces (2016, methodology): “r p,q and w holds, if there exists a constant C > 0 such that (2) Z∞ 1 1 Φ p,q,w(sQ) ds s ≤ C Φ (Q) (Q ∈ Q) holds. Note that the weighted integral condition (2) for p,q and w implies w ∈ Bp,q; see [30] for details. Using these two notions, we aim to give the suﬃciently conditions of the boundedne”