Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class

  • S. H. Saker Mansoura University and New Mansoura University, Egypt
  • R. R. Mahmoud Rustaq College of Education, Rustaq-Sultanate of Oman and Faculty of Science, Fayoum University, Egypt
  • M. H. Hassan Mansoura University, Egypt
Keywords: Gehring class, Muckenhoupt class, Hardy inequality, Carleman inequality.


UDC 517.5

We prove some relations between the discrete Gehring classes $\mathcal{G}_{q}$ and the discrete Muckenhoupt classes  $\mathcal{A}_{p}.$  Specifically, by using some known Hardy-type and Carleman-type inequalities, we study the relationship between $\mathcal{G}_{1},$ $\mathcal{A}_{\infty }$ and $\mathcal{A}_{1}$ for nonincreasing and nondecreasing weights.  Finally, we establish some general results by introducing the notions of $\mathcal{G}_{\varphi }$ classes defined for nonnegative convex function $\varphi.$


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How to Cite
SakerS. H., MahmoudR. R., and HassanM. H. “Quantitative Dependence of Some Discrete Limiting Classes on the Muckenhoupt ${\cal A}_1(u)$ Class”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 3, Apr. 2023, pp. 397 -15, doi:10.37863/umzh.v75i3.6788.
Research articles