Quantitative Dependence of Some Discrete Limiting Classes on the Muckenhoupt 풜1(u) Class.

We prove some relations between the discrete Gehring classes 풢q and discrete Muckenhoupt classes 풜p. Specifically, by using some known Hardy-type and Carleman-type inequalities, we study the relationship between 풢1, 풜∞, and 풜1 for nonincreasing and nondecreasing weights. Finally, we establish some general results by introducing the notions of 풢φ classes defined for a nonnegative convex function φ. [ABSTRACT FROM AUTHOR]