The title says it all;
Is there a concept of orthogonality of functions where the functions are of several variables?
For example, according to the wikipedia page on orthogonal functions, functions $f$ and $g$ are orthogonal if
$$\left<f, g \right> = \int_If(x)g(x)\ dx = 0$$
where $I$ is an interval. What if we have $f(x,y)$ and $g(x,y)$ and some domain $D$? Can we say that $f$ and $g$ are orthogonal on $D$ if
$$\iint_D f(x,y)g(x,y)\ dxdy = 0$$