Abstract
In this chapter we give a complete characterization of the range I α[L p (.)(ℝn)] in terms of the convergence of hypersingular integrals of order α. The proof is based, in particular, on the results on denseness in L p (.)(ℝn) of Schwartz functions orthogonal to polynomials, and the inversion of the Riesz potential operator by means of hypersingular integrals.
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© 2016 Springer International Publishing Switzerland
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Kokilashvili, V., Meskhi, A., Rafeiro, H., Samko, S. (2016). Description of the Range of Potentials, and Hypersingular Integrals. In: Integral Operators in Non-Standard Function Spaces. Operator Theory: Advances and Applications, vol 248. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21015-5_7
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DOI: https://doi.org/10.1007/978-3-319-21015-5_7
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-21014-8
Online ISBN: 978-3-319-21015-5
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