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Non-smooth atomic decomposition for generalized Orlicz-Morrey spaces. (English) Zbl 1326.41021

Summary: In the present paper, we consider the non-smooth atomic decomposition of generalized Orlicz-Morrey spaces. The result will be sharper than the existing results. As an application, we consider the boundedness of the bilinear operator, which is called the Olsen inequality nowadays. To obtain a sharp norm estimate, we first investigate their predual space, which is even new, and we make full advantage of the vector-valued inequality for the Hardy-Littlewood maximal operator.

MSC:

41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
42B25 Maximal functions, Littlewood-Paley theory
42B35 Function spaces arising in harmonic analysis
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