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Calderón-Zygmund operators with kernels of Dini’s type on generalized weighted variable exponent Morrey spaces

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Abstract

Let T be a Calderón-Zygmund operator of type \(\omega \) with \(\omega (t)\) being nondecreasing and satisfying a kind of Dini’s type condition and let \(T_{\vec {b}}\) be the multilinear commutators of T with \(BMO^m\) functions. In this paper, we study the boundedness of the operators T and \(T_{\vec {b}}\) on generalized weighted variable exponent Morrey spaces \(M^{p(\cdot ),\varphi }(w)\) with the weight function w belonging to variable Muckenhoupt’s class \(A_{p(\cdot )}({{\mathbb {R}}^n})\). We find the sufficient conditions on the pair \((\varphi _1,\varphi _2)\) with \(\vec {b} \in BMO^m({{\mathbb {R}}^n})\) which ensures the boundedness of the operators T and \(T_{\vec {b}}\) from \(M^{p(\cdot ),\varphi _1}(w)\) to \(M^{p(\cdot ),\varphi _2}(w)\).

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Acknowledgements

The author would like to express their gratitude to the referees for his very valuable comments and suggestions. The research of author was partially supported by grant of Cooperation Program 2532 TUBITAK - RFBR (RUSSIAN foundation for basic research) (Agreement number no. 119N455), by Grant of 1st Azerbaijan-Russia Joint Grant Competition (Agreement Number No. EIF-BGM-4-RFTF-1/2017-21/01/1-M-08) and by the RUDN University Strategic Academic Leadership Program.

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  1. Institute of Applied Mathematics, Baku State University, Baku, AZ1148, Azerbaijan

    V. S. Guliyev

  2. Department of Mathematics, Dumlupinar University, 43020, Kutahya, Turkey

    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. Calderón-Zygmund operators with kernels of Dini’s type on generalized weighted variable exponent Morrey spaces. Positivity 25, 1771–1788 (2021). https://doi.org/10.1007/s11117-021-00846-1

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