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Global regularity in Orlicz–Morrey spaces of solutions to parabolic equations with VMO coefficients

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Abstract

We show continuity in generalized parabolic Orlicz–Morrey spaces \(M^{\varPhi ,\varphi }\) of sublinear integral operators generated by parabolic Calderón–Zygmund operator and their commutators with BMO functions. As a consequence, we obtain a global \(M^{\varPhi ,\varphi }\)-regularity result for the Cauchy–Dirichlet problem for linear uniformly parabolic equations with vanishing mean oscillation coefficients.

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Acknowledgements

The research of V. Guliyev and M. Omarova was partially supported by the Grant of 1st Azerbaijan-Russia Joint Grant Competition (Agreement Number No. EIF-BGM-4-RFTF-1/2017-21/01/1).

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Authors and Affiliations

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

    Vagif Guliyev, Ismail Ekincioglu & Aysel Ahmadli

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

    Vagif Guliyev

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

    Vagif Guliyev & Mehriban Omarova

  4. Baku State University, Baku, Azerbaijan

    Mehriban Omarova

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  1. Vagif Guliyev
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  2. Ismail Ekincioglu
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  3. Aysel Ahmadli
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  4. Mehriban Omarova
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Correspondence to Vagif Guliyev.

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Guliyev, V., Ekincioglu, I., Ahmadli, A. et al. Global regularity in Orlicz–Morrey spaces of solutions to parabolic equations with VMO coefficients. J. Pseudo-Differ. Oper. Appl. 11, 1963–1989 (2020). https://doi.org/10.1007/s11868-019-00325-y

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