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Spherical convolution operators in spaces of variable Hölder order

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Abstract

In this paper, we study the images of operators of the type of spherical potential of complex order and of spherical convolutions with kernels depending on the inner product and having a spherical harmonic multiplier with a given asymptotics at infinity. Using theorems on the action of these operators in Hölder-variable spaces, we construct isomorphisms of these spaces. In Hölder spaces of variable order, we study the action of spherical potentials with singularities at the poles of the sphere. Using stereographic projection, we obtain similar isomorphisms of Hö lder-variable spaces with respect to n-dimensional Euclidean space (in the case of its one-point compactification) with some power weights.

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Authors and Affiliations

  1. Rostov State University, Russia

    B. G. Vakulov

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  1. B. G. Vakulov
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__________

Translated from Matematicheskie Zametki, vol. 80, no. 5, 2006, pp. 683–695.

Original Russian Text Copyright © 2006 by B. G. Vakulov.

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Vakulov, B.G. Spherical convolution operators in spaces of variable Hölder order. Math Notes 80, 645–657 (2006). https://doi.org/10.1007/s11006-006-0185-5

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