Generalized Localization Principle for Continuous Wavelet Decompositions

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 $L_p$ 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.