A generalisation of Chui's window functions and its boundedness property (Q2917757)

The authors give a new proof of the following fact which is relevant for wavelet analysis: if \(f\in L^2(\mathbb R^n)\) and the functions \((x_1,\dotsc, x_n)\mapsto \left (\prod_{j\in J} x_j \right )f(x_1,\dotsc, x_n)\) belong to \( L^2(\mathbb R^n)\) for each \(J\subset \{1,\dotsc,n\}\), then \(f\in L^1(\mathbb R^n)\).