Hardy's inequality in power-type weighted Lp(⋅)(0,∞) spaces

In this article, our aim is to prove Hardy's inequality in power-type weighted Lp(⋅)(0,∞) spaces by obtaining regularity condition on the exponents p(⋅), q(⋅) and α(⋅) defined at every point of the domain of test function with u(0)=0 (or vanishing at infinity) under the log-Hölder continuity conditions at the origin and infinity.