Suppose that $g,h : \mathbb{R} \rightarrow \mathbb{R}^+$ and $f: \mathbb{R}^2 / \left\{(0,0)\right\} \rightarrow \mathbb{R}^+$ and that $g(x_1) \le f(x_1,x_2) \le h(x_1)$ where not both $x_1,x_2$ are zero and suppose that $\lim_{x_1 \rightarrow 0}g(x_1) = \lim_{x_1 \rightarrow 0} h(x_1)=L$. Can we then conclude that $\lim_{x_1 \rightarrow 0, x_2 \rightarrow 0} f(x_1,x_2) = L$?
In particular, does there exist a generalized Squeeze/Sandwich Theorem for functions of more than one variable?