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Commutators of parabolic fractional integrals with variable kernels in vanishing generalized variable Morrey spaces

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Abstract

We obtain the boundedness of parabolic fractional integral operators \(T_{\Omega ,\alpha }\) with variable kernels \(\Omega (\cdot ,\cdot )\) belonging to \(L^{\infty }({\mathbb {R}^n}) \times L^{s}({\mathbb {S}}^{n-1}), s>n/(n-\alpha )\), and their commutators \([b,T_{\Omega ,\alpha }]\) with BMO functions in variable exponent generalized Morrey spaces \(M^{p(\cdot ),\varphi }\) and variable exponent vanishing generalized Morrey spaces \(\textrm{VM}^{p(\cdot ),\varphi }\). We find the sufficient conditions on the pair \((\varphi ,\psi )\) which ensures the boundedness of the operators \(T_{\Omega ,\alpha }\) and \([b,T_{\Omega ,\alpha }]\) from \(M^{p(\cdot ),\varphi }\) to \(M^{q(\cdot ),\psi }\) and from \(\textrm{VM}^{p(\cdot ),\varphi }\) to \(\textrm{VM}^{q(\cdot ),\psi }\).

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Acknowledgements

The research of I. Ekincioglu and A. Serbetci was partially supported by grant of Cooperation Program 2532 TUBITAK - RFBR (RUSSIAN foundation for basic research) (Agreement Number No. 119N455). The authors are grateful to the referee for his/her invaluable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Dumlupinar University, Kutahya, Turkey

    I. Ekincioglu

  2. Department of Mathematics, Istanbul Medeniyet University, Istanbul, Turkey

    I. Ekincioglu

  3. Azerbaijan State Pedagogical University, AZ1000, Baku, Azerbaijan

    S. Z. Khaligova

  4. Department of Mathematics, Ankara University, Ankara, Turkey

    A. Serbetci

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  1. I. Ekincioglu
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  2. S. Z. Khaligova
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  3. A. Serbetci
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Correspondence to A. Serbetci.

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Ekincioglu, I., Khaligova, S.Z. & Serbetci, A. Commutators of parabolic fractional integrals with variable kernels in vanishing generalized variable Morrey spaces. Positivity 26, 82 (2022). https://doi.org/10.1007/s11117-022-00947-5

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