| Abstract: |
| In this short note we prove the existence of local fractal functions of the Hardy-Orlicz class. The graph of a local fractal function coincides with the attractor of an appropriate iterated function system, whose construction is fairly standard. Local fractal functions appear naturally as the fixed points of the Read-Bajraktarevi\`c operator when restricted to a suitable Orlicz-Sobolev space. Our results extend some of the outcomes obtained by Massopust on Lebesgue and Sobolev spaces to higher order, dimension and function spaces (where the role of the norm is now played by a Young function). |
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