In this paper, we study the relationship between the Muckenhoupt class A α 1 (C) and the Gehring class G α q (K) via conformable calculus. We also establish the constants of the classes for the power law functions.

In this paper, we prove some reverse conformable inequalities with weights and employ them to prove some conformable inequalities of Gehring type. Moreover, we prove some interpolation theorems which are powerful tools in the study of operators in function spaces. Our results develop a technique based on the applications of a refinement of conformable inequalities.