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Commutators of multilinear Calderón–Zygmund operators with kernels of Dini’s type on generalized weighted Morrey spaces and applications

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Abstract

Let T be a multilinear Calderón–Zygmund operator of type \(\omega \) with \(\omega \) being nondecreasing and satisfying a kind of Dini’s type condition and \(T_{\Pi \vec {b}}\) be the iterated commutators of the operator T with \(BMO^m\) functions. The generalized weighted Morrey strong and weak \(L(\log L)\)-type endpoint estimates for T and \(T_{\Pi \vec {b}}\) with multiple weights are established. As applications multiple weighted Morrey estimates for iterated commutators of bilinear pseudo-differential operators and paraproducts with mild regularity are given.

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Acknowledgements

The author thanks the referee(s) for careful reading the paper and useful comments. The research of V. Guliyev was partially supported by the grant of Cooperation Program 2532 TUBITAK - RFBR (RUSSIAN foundation for basic research) (Agreement number no. 119N455) and by the RUDN University Strategic Academic Leadership Program.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan

    V. S. Guliyev

  2. Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan

    V. S. Guliyev

  3. Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, Russian Federation, 117198

    V. S. Guliyev

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Guliyev, V.S. Commutators of multilinear Calderón–Zygmund operators with kernels of Dini’s type on generalized weighted Morrey spaces and applications. Positivity 27, 13 (2023). https://doi.org/10.1007/s11117-022-00963-5

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