Characterizations for the fractional maximal operator and its commutators on total Morrey spaces

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发表日期：

2024年7月11日

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V. S. Guliyev

摘要

We shall give a characterization for the strong and weak type Adams type boundedness of the fractional maximal operator $M_{\alpha }$ $M_{α}$ on total Morrey spaces $L^{p,\lambda ,\mu }(\mathbb {R}^n)$ $L^{p, λ, μ} (R^{n})$ , respectively. Also we give necessary and sufficient conditions for the boundedness of the fractional maximal commutator operator $M_{b,\alpha }$ $M_{b, α}$ and commutator of fractional maximal operator $[b,M_{\alpha }]$ $[b, M_{α}]$ on $L^{p,\lambda ,\mu }(\mathbb {R}^n)$ $L^{p, λ, μ} (R^{n})$ when b belongs to $BMO(\mathbb {R}^n)$ $B M O (R^{n})$ spaces, whereby some new characterizations for certain subclasses of $BMO(\mathbb {R}^n)$ $B M O (R^{n})$ spaces are obtained.