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 Mat. Zametki, 2006, Volume 80, Issue 5, Pages 683–695 (Mi mz3077)

Spherical convolution operators in spaces of variable Hölder order

B. G. Vakulov

Rostov State University

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 Hölder-variable spaces with respect to $n$-dimensional Euclidean space (in the case of its one-point compactification) with some power weights.

DOI: https://doi.org/10.4213/mzm3077

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English version:
Mathematical Notes, 2006, 80:5, 645–657

Bibliographic databases:

UDC: 517.518

Citation: B. G. Vakulov, “Spherical convolution operators in spaces of variable Hölder order”, Mat. Zametki, 80:5 (2006), 683–695; Math. Notes, 80:5 (2006), 645–657

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz3077
• https://doi.org/10.4213/mzm3077
• http://mi.mathnet.ru/eng/mz/v80/i5/p683

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Almeida A., Samko S., “Embeddings of variable Hajłasz-Sobolev spaces into Hölder spaces of variable order”, J. Math. Anal. Appl., 353:2 (2009), 489–496
2. Samko N., “Parameter depending almost monotonic functions and their applications to dimensions in metric measure spaces”, J. Funct. Spaces Appl., 7:1 (2009), 61–89
3. B. G. Vakulov, E. S. Kochurov, “Operatory drobnogo integrirovaniya i differentsirovaniya peremennogo poryadka v prostranstvakh Geldera $H^{\omega(t,x)}$”, Vladikavk. matem. zhurn., 12:4 (2010), 3–11
4. Samko N., Samko S., Vakulov B., “Fractional integrals and hypersingular integrals in variable order Holder spaces on homogeneous spaces”, J. Funct. Spaces Appl., 8:3 (2010), 215–244
5. B. G. Vakulov, E. S. Kochurov, N. G. Samko, “Zygmund-type estimates for fractional integration and differentiation operators of variable order”, Russian Math. (Iz. VUZ), 55:6 (2011), 20–28
6. Samko N., Vakulov B., “Spherical fractional and hypersingular integrals of variable order in generalized Holder spaces with variable characteristic”, Math. Nachr., 284:2-3 (2011), 355–369
7. Diening L., Samko S.G., “On Potentials in Generalized Holder Spaces Over Uniform Domains in R-N”, Rev. Mat. Complut., 24:2 (2011), 357–373
8. Samko S.G., “Potential Operators in Generalized Holder Spaces on Sets in Quasi-Metric Measure Spaces Without the Cancellation Property”, Nonlinear Anal.-Theory Methods Appl., 78 (2013), 130–140
9. Samko S., “Fractional Integration and Differentiation of Variable Order: an Overview”, Nonlinear Dyn., 71:4, SI (2013), 653–662
10. Rafeiro H., Samko S., “Fractional integrals and derivatives: mapping properties”, Fract. Calc. Appl. Anal., 19:3 (2016), 580–607
11. Kokilashvili V. Meskhi A. Rafeiro H. Samko S., “Integral Operators in Non-Standard Function Spaces, Vol 1: Variable Exponent Lebesgue and Amalgam Spaces”, Integral Operators in Non-Standard Function Spaces, Vol 1: Variable Exponent Lebesgue and Amalgam Spaces, Operator Theory Advances and Applications, 248, Springer Int Publishing Ag, 2016, 1–567
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