Quantitative dependence of some discrete limiting classes on the Muckenhoupt \calA 1 ( u ) class

UDC 517.5 We prove some relations between the discrete Gehring classes 𝒢 q and the discrete Muckenhoupt classes 𝒜 p . Specifically, by using some known Hardy-type and Carleman-type inequalities, we study the relationship between 𝒢 1 , 𝒜 ∞ and 𝒜 1 for nonincreasing and nondecreasing weights. Finally, we establish some general results by introducing the notions of 𝒢 φ classes defined for nonnegative convex function φ .