  In this paper, we prove the Hardy-Leray inequality and related
  inequalities in variable Lebesgue spaces. Our proof is based on a
  version of the Stein-Weiss inequality in variable Lebesgue spaces
  derived from two weight inequalities due to Melchiori and Pradolini. We also
discuss an application of our results to establish an existence result for the
degenerate $\pp$-Laplace operator.
