image processing - Is it possible to simplify the convolution integral if the functions are non-zero in disjoint areas?

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When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start?

I have a function $f(x,y)$ and $h(x,y)$. $f(x,y)$ has a value of $\frac{1}{3}$ when $x$ is between $\frac{1}{3}$ and $\frac{5}{9}$, and $y$ is between $0$ and $1$. The function has a value of $0$ everywhere else. Meanwhile, $h(x,y)$ has a value of 1 when both $x$ and $y$ are between $-\frac{1}{19}$ and $\frac{1}{19}$.

These two functions are non-zero in completely disjoint regions. Is there a way to leverage this property to simplify the convolution integral?