On Paley-type theorems for multidimensional Fourier series on generalized Haar-type systems

In the paper we prove Paley-type theorems for multidimensional Fourier series on generalized Haar-type systems under the boundedness condition of their generating number sequences. Properties of base of product of generalized Haar-type systems in $L_p[0,1]^n$ are proved. Then, using them, the Paley-type theorems on Fourier coefficients are obtained. Comparisons of our results with the known statements are also given.