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In this paper we study existence and uniqueness of solutions for the Hammerstein equation $$u\left(x\right)=v\left(x\right)+\lambda {\int }_{I_a^b}K(x,y)f(y,u\left(y\right))dy,x\in I_a^b:=[a_1,b_1]\times [a_2,b_2],$$ in the space $B{V}_{\varphi }^{ℝ}\left(I_a^b\right)$ of function of bounded total $\varphi -$variation in the sense of Riesz, where $\lambda \in ℝ$, $K:I_a^b\times I_a^b\to ℝ$ and $f:I_a^b\times ℝ\to ℝ$ are suitable functions.