Quantitative dependence of some discrete limiting classes on the Muckenhoupt ${\cal A}_1(u)$ class - Saker, S. H.; Mahmoud, R. R.; Hassan, M. H. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 517.5We 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 $\mathcal{G}_{1},$ $\mathcal{A}_{∞ }$ and $\mathcal{A}_{1}$ for nonincreasing and nondecreasing weights. Finally, we establish some general results by introducing the notions of $\mathcal{G}_{φ }$ classes defined for nonnegative convex function $φ.$