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  • 1.
    Kolyada, Viktor
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Embedding theorems for Sobolev and Hardy-Sobolev spaces and estimates of Fourier transforms2019In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 198, no 2, p. 615-637Article in journal (Refereed)
    Abstract [en]

    We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvement of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin-type estimates of Fourier transforms for functions in Sobolev spaces W11(Rn).

  • 2.
    Kolyada, Viktor
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Optimal relationships between L-p-norms for the Hardy operator and its dual2014In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 193, no 2, p. 423-430Article in journal (Refereed)
    Abstract [en]

    We obtain sharp two-sided inequalities between -norms of functions and , where is the Hardy operator, is its dual, and is a nonnegative measurable function on In an equivalent form, it gives sharp constants in the two-sided relationships between -norms of functions and , where is a nonnegative nonincreasing function on with In particular, it provides an alternative proof of a result obtained by Kruglyak and Setterqvist (Proc Am Math Soc 136:2005-2013, 2008) for and by Boza and Soria (J Funct Anal 260:1020-1028, 2011) for all , and gives a sharp version of this result for 1 < p < 2.

  • 3.
    Kolyada, Viktor
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Soria, Javier
    Hölder type inequalities in Lorentz spaces2010In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 189, no 3, p. 523-538Article in journal (Refereed)
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