Non‐smooth atomic decomposition for generalized Orlicz‐Morrey spaces |
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Authors: | Yoshihiro Sawano Denny Ivanal Hakim Hendra Gunawan |
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Institution: | 1. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Hachioji‐shi, Tokyo, Japan;2. Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia |
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Abstract: | 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. |
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Keywords: | Generalized Orlicz‐Morrey spaces atomic decomposition maximal operators 41A17 42B25 42B35 |
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