Weighted Hardy operators in local generalized Orlicz-Morrey spaces

  • C. Aykol Department of Mathematics, Ankara University, Ankara, Turkey
  • Z.O. Azizova Azerbaijan State Oil and Industry University, Baku, Azerbaijan
  • J.J. Hasanov Azerbaijan State Oil and Industry University, Baku, Azerbaijan
Keywords: weighted Hardy operator, local generalized Orlicz-Morrey space, local $BMO$ space
Published online: 2021-11-06

Abstract


In this paper, we find sufficient conditions on general Young functions $(\Phi, \Psi)$ and the functions $(\varphi_1,\varphi_2)$ ensuring that the weighted Hardy operators $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ are of strong type from a local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ into another local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$. We also obtain the boundedness of the commutators of $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ from $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ to $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$.

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How to Cite
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AykolC.; AzizovaZ.; HasanovJ. Weighted Hardy Operators in Local Generalized Orlicz-Morrey Spaces. Carpathian Math. Publ. 2021, 13, 522-533.