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The Definition of a Self-Similar function in Quasi-Banach Spaces

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Abstract

The definition of a self-similar function is extended to quasi-Banach Lebesgue spaces. A sufficient condition for a function with given self-similarity parameters to lie in some such space is given.

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References

  1. I. A. Sheipak, “On the construction and some properties of self-similar functions in the spacesL p[0, 1],” Mat. Zametki 81 (6), 924–938 (2007) [Math. Notes 81 (6), 827–839 (2007)].

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Funding

This work was supported by the Russian Science Foundation under grant 17-11-01215.

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Authors and Affiliations

  1. Advanced Educational Scientific Center of Lomonosov Moscow State University, “Kolmogorov School,”, Moscow, 121357, Russia

    Yu. V. Tikhonov

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  1. Yu. V. Tikhonov
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Correspondence to Yu. V. Tikhonov.

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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 6, pp. 917–923.

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Tikhonov, Y.V. The Definition of a Self-Similar function in Quasi-Banach Spaces. Math Notes 106, 980–985 (2019). https://doi.org/10.1134/S0001434619110348

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  • DOI: https://doi.org/10.1134/S0001434619110348

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