Geodesic
On the Construction and Some Properties of Self-Similar Functions in the Spaces $L_p[0,1]$
Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 924-938

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We present a construction of affinely self-similar functions. In terms of the parameters of self-similarity transformations, a condition is given for these functions to belong to the classes $L_p[0,1]$ as well as to the space $C[0,1]$. Some properties of these functions (monotonicity and bounded variation) are studied. A relationship between self-similar functions and self-similar measures is established.
Keywords: self-similar function, self-similar measure, fractal curve, monotonicity, function of bounded variation
Mots-clés : Lebesgue classes. 
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     author = {I. A. Sheipak},
     title = {On the {Construction} and {Some} {Properties} of {Self-Similar} {Functions} in the {Spaces} $L_p[0,1]$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {924--938},
     publisher = {mathdoc},
     volume = {81},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a10/}
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I. A. Sheipak. On the Construction and Some Properties of Self-Similar Functions in the Spaces $L_p[0,1]$. Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 924-938. http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a10/