Let \(\mathbb{D}\) denote the open unit disk and let \(dA\) denote the normalized Lebesgue measure on \(\mathbb{D}\). The Bergman space is defined by \({\mathcal L}_ a^ p=\{f\); \(f:\mathbb{D}\to\mathbb{C}\), \(f\) analytic and \(\int_ D| f(z)|^ 2 dA(z)<\infty\}\). The maximum ideal space of the Banach algebra of bounded analytic functions on \(\mathbb{D}\) is denoted by \({\mathcal M}\). Let \({\mathcal U}\) be the algebra of functions on \(\mathbb{D}\) which can be extended continuously to \({\mathcal M}\) and let \(G\) be the union of all non- trivial Gleason parts of \({\mathcal M}\setminus\mathbb{D}\). A space of functions contained in \({\mathcal L}^ \infty(\mathbb{D})\cap C(\mathbb{D}\cup G)\), but not necessarily in \({\mathcal U}\), is considered. The paper gives a representation of these functions as bounded multiplication operators on \({\mathcal L}_ a^ 2\) and identifies the subspace consisting of functions which induce compact multiplication operators.