The objective of this article is to broaden the understanding of the connections between bent functions and partial difference sets. Recently, the first two authors showed that the elements which a vectorial dual-bent function with certain additional properties maps to 0, form a partial difference set, which generalizes the connection between Boolean bent functions and Hadamard difference sets, and some later established connections between p-ary bent functions and partial difference sets to vectorial bent functions. We discuss the effects of coordinate transformations. As all currently known vectorial dual-bent functions F:Fpn→Fps\documentclass[12pt]{minimal}
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\begin{document}$$F:{\mathbb {F}}_{p^n}\rightarrow {\mathbb {F}}_{p^s}$$\end{document} are linear equivalent to l-forms, i.e., to functions satisfying F(βx)=βlF(x)\documentclass[12pt]{minimal}
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\begin{document}$$F(\beta x) = \beta ^lF(x)$$\end{document} for all β∈Fps\documentclass[12pt]{minimal}
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\begin{document}$$\beta \in {\mathbb {F}}_{p^s}$$\end{document}, we investigate properties of partial difference sets obtained from l-forms. We show that they are unions of cosets of Fps∗\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_{p^s}^*$$\end{document}, which also can be seen as certain cyclotomic classes. We draw connections to known results on partial difference sets from cyclotomy. Motivated by experimental results, for a class of vectorial dual-bent functions from Fpn\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_{p^n}$$\end{document} to Fps\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_{p^s}$$\end{document}, we show that the preimage set of the squares of Fps\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {F}}_{p^s}$$\end{document} forms a partial difference set. This extends earlier results on p-ary bent functions.
