Abstract
In this paper we prove that the Hardy–Littlewood maximal operator is bounded on Morrey spaces \({\mathcal{M}_{1,\lambda}(\mathbb{R}^n)}\), \({0 \le \lambda < n}\) for radial, non-increasing functions on \({\mathbb{R}^n}\).
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The research of A. Gogatishvili was partly supported by the Grants P201-13-14743S of the Grant Agency of the Czech Republic and RVO: 67985840, by Shota Rustaveli National Science Foundation Grants No. 31/48 (Operators in some function spaces and their applications in Fourier Analysis) and No. DI/9/5-100/13 (Function spaces, weighted inequalities for integral operators and problems of summability of Fourier series). The research of A. Gogatishvili and R. Ch. Mustafayev was partly supported by the joint project between Academy of Sciences of Czech Republic and The Scientific and Technological Research Council of Turkey.
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Gogatishvili, A., Mustafayev, R.C. A Note on Boundedness of the Hardy–Littlewood Maximal Operator on Morrey Spaces. Mediterr. J. Math. 13, 1885–1891 (2016). https://doi.org/10.1007/s00009-015-0614-3
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DOI: https://doi.org/10.1007/s00009-015-0614-3