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Generalized Localization Principle for Continuous Wavelet Decompositions

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Abstract

Spherically symmetric continuous wavelet decompositions are considered, and the notion of Riesz means is introduced for them. Generalized localization is proved for the decompositions under study in Lp classes without any restrictions on the wavelets. Further, generalized localization is studied for the Riesz means of wavelet decompositions of distributions from the Sobolev class with negative order of smoothness.

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Acknowledgments

The author wishes to express gratitude to Sh. A. Alimov for discussions of the results.

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Correspondence to R. R. Ashurov or Yu. É. Faiziev.

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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 6, pp. 803-810.

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Ashurov, R.R., Faiziev, Y.É. Generalized Localization Principle for Continuous Wavelet Decompositions. Math Notes 106, 857–863 (2019). https://doi.org/10.1134/S0001434619110208

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  • DOI: https://doi.org/10.1134/S0001434619110208

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