Fractal surfaces in Lebesgue spaces with respect to fractal measures and associated fractal operators

Abstract

The goal of this article is to study the fractal surfaces and associated fractal operator on Lebesgue spaces with respect to fractal measures. First, we show that fractal surfaces belongs to Lebesgue spaces under certain conditions. Then, we define a fractal operator on Lebesgue spaces and discuss some analytical properties of it. Moreover, we show the existence of Schauder basis of the associated fractal functions for the space L q ( I × J , μ p ) . In the end, we draw some graph of fractal surfaces for the various scaling factors and mention some future directions.

Topics & Concepts