Abstract
We consider generalized Orlicz–Morrey spaces \(M_{\Phi},\varphi\,(\mathbb{R}_{n})\) including their weak versions. In these generalized spaces we prove the boundedness of the Hardy–Littlewood maximal operator and Calderón–Zygmund singular operators with standard kernel. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on \(\varphi(r)\) without assuming any monotonicity property of \(\varphi(r)\) , or in terms of supremal operators, related to \(\varphi(r)\).
Mathematics Subject Classification (2010). Primary 42B20, 42B25, 42B35.
Dedicated to Professor António Ferreira dos Santos
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Deringoz, F., Guliyev, V.S., Samko, S. (2014). Boundedness of the Maximal and Singular Operators on Generalized Orlicz–Morrey Spaces. In: Bastos, M., Lebre, A., Samko, S., Spitkovsky, I. (eds) Operator Theory, Operator Algebras and Applications. Operator Theory: Advances and Applications, vol 242. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0816-3_7
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DOI: https://doi.org/10.1007/978-3-0348-0816-3_7
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