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Estimates for operators on generalized weighted Orlicz-Morrey spaces and their applications to non-divergence elliptic equations

Abstract

We show continuity in generalized weighted Orlicz-Morrey spaces \(M^{\Phi ,\varphi }_{w}\) of sublinear integral operators generated by some classical integral operators and commutators. The obtained estimates are used to study global regularity of the solution of the Dirichlet problem for linear uniformly elliptic operators with discontinuous data.

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Acknowledgements

The authors thank the referee(s) for careful reading the paper and useful comments. The research of Guliyev was partially supported by 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. The research of Omarova was partially supported by Grant of 1st Azerbaijan-Russia Joint Grant Competition (Agreement Number No. EIF-BGM-4-RFTF-1/2017-21/01/1-M-08).

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Guliyev, V.S., Omarova, M.N. Estimates for operators on generalized weighted Orlicz-Morrey spaces and their applications to non-divergence elliptic equations. Positivity 26, 40 (2022). https://doi.org/10.1007/s11117-022-00896-z

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  • DOI: https://doi.org/10.1007/s11117-022-00896-z

Keywords

  • Generalized weighted Orlicz-Morrey spaces
  • Muckenhoupt weight
  • Sublinear integrals
  • Calderón-Zygmund integrals
  • Commutators
  • VMO
  • Elliptic equations
  • Dirichlet problem

Mathematics Subject Classification

  • 35J25
  • Secondary 35B45
  • 42B20
  • 42B35
  • 46E30