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 Eurasian Math. J., 2021, Volume 12, Number 2, Pages 10–18 (Mi emj399)

Modulus of continuity for Bessel type poteniial over Lorentz space

N. H. Alkhalil

S.M. Nikol’skii Mathematical Institute Peoples Friendship University of Russia 6 Miklukho Maklai St, 117198, Moscow, Russia Federation

Abstract: The generalized Bessel potentials are constructed using convolutions of the generalized Bessel–McDonald kernels with functions belonging to a basic rearrangement invariant space. Under assumptions ensuring the embedding of potentials into the space of bounded continuous functions, differential properties of potentials are described by using the $k$-th order modulus of continuity in the uniform norm. In the paper, estimates are given for the $k$-th order modulus of continuity in the uniform norm in the case of the generalized Bessel potentials constructed over the basic weighted Lorentz space.

Keywords and phrases: the generalized Bessel potential, the modulus of continuity of a potential, Lorentz space, rearrangement invariant space.

DOI: https://doi.org/10.32523/2077-9879-2021-12-2-10-18

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MSC: 46A30, 42A16
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Citation: N. H. Alkhalil, “Modulus of continuity for Bessel type poteniial over Lorentz space”, Eurasian Math. J., 12:2 (2021), 10–18

Citation in format AMSBIB
\Bibitem{Alk21} \by N.~H.~Alkhalil \paper Modulus of continuity for Bessel type poteniial over Lorentz space \jour Eurasian Math. J. \yr 2021 \vol 12 \issue 2 \pages 10--18 \mathnet{http://mi.mathnet.ru/emj399} \crossref{https://doi.org/10.32523/2077-9879-2021-12-2-10-18} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85111488124}