On the graphs of products of continuous functions and fractal dimensions

In this paper, we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions. More precisely, we show that, given a real number 1 ≤ β ≤ 2, any real-valued continuous function in C([0, 1]) can be decomposed into a product of two real-valued continuous functions, each having a graph of Hausdorff dimension β. In addition, a product decomposition result for the packing dimension is obtained. This work answers affirmatively two questions raised by Verma and Priyadarshi [14].