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The multisublinear maximal type operators in Banach function lattices |
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| Authors: | Vakhtang Kokilashvili Mieczysław Mastyło Alexander Meskhi |
| Institution: | 1. A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 6. Tamarashvili Str., Tbilisi 0177, Georgia;2. International Black Sea University, 3 Agmashenebeli Ave., Tbilisi 0131, Georgia;3. Adam Mickiewicz University and Institute of Mathematics, Polish Academy of Science (Poznań branch), Umultowska 87, 61-614 Poznań, Poland;4. Department of Mathematics, Faculty of Informatics and Control Systems, Georgian Technical University, 77, Kostava St., Tbilisi, Georgia |
| Abstract: | The main aim of this paper is to study a general multisublinear operators generated by quasi-concave functions between weighted Banach function lattices. These operators, in particular, generalize the Hardy–Littlewood and fractional maximal functions playing an important role in harmonic analysis. We prove that under some general geometrical assumptions on Banach function lattices two-weight weak type and also strong type estimates for these operators are true. To derive the main results of this paper we characterize the strong type estimate for a variant of multilinear averaging operators. As special cases we provide boundedness results for fractional maximal operators in concrete function spaces. |
| Keywords: | Banach function lattices Multilinear operators Fractional integrals Two-weight inequality |
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