In this paper, we discuss about the boundedness of the Laplace transform \(\mathcal{L}: L_p([0,\infty))\rightarrow L_p(A)\) (\(p\geq1\)) for the cases \(A=[0, \infty)\), \(A=[1, \infty)\) and \(A=[0, 1]\). We also provide examples for the cases where \(\mathcal{L}\) is unbounded.
