  In this article we will prove that if the continuous closed curve $\gamma :
[0, 1] \rightarrow \mathbb{R}^2$ has finite $p$-variation with $p < 2$, then
$(\iint\limits_{\mathbb{R}^2}|\eta(\gamma, (x, y))|^q \,dx \,dy)^{1/q} \le
(\frac{1}{2})^\frac{1}{q}(\zeta(\frac{2}{pq})-1)(||\gamma||_{p, [0,
1]})^{\frac{2}{q}} $ for all $q \in [1, \frac{2}{p})$, where $\eta(\gamma, (x,
y))$ is the winding number of $\gamma$ at $(x, y), \zeta$ is the Reimann zeta
function, and $||\gamma||_{p, [0, 1]}$ is the $p$-variation of $\gamma$ on the
interval $[0, 1]$.
  Our main contribution is that we have explicitly given a bound by known
constants, and we have found this by an elementary proof. We are going to be
using a method introduced by L.C. Young in 1936.
