We study the refinements of several well-known local fractional Hilbert-type inequalities obtained by interpolating the Lebesgue norms of local fractional Laplace transforms of the functions involved in these inequalities. As an application, the main results are compared with some our results previously known from the literature.
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Ts. Batbold, M. Krnić, and P. Vuković, “A unified approach to fractal Hilbert-type inequalities,” J. Inequal. Appl., 2019, Article 117 (2019).
Ts. Batbold, M. Krnić,, J. Pečarić,, and P. Vuković,, Further Development of Hilbert-Type Inequalities, Element, Zagreb (2017).
G.-S. Chen, “Generalizations of Hölder’s and some related integral inequalities on fractal space,” J. Funct. Spaces Appl., 2013 (2013).
G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, Cambridge (1967).
G. Jumarie, “Fractional Euler’s integrals of first and second kinds. Application to fractional Hermite’s polynomials and to probability density of fractional order,” J. Appl. Math. Inform., 28, No. 1-2, 257 – 273 (2010).
M. Krnić,, J. Pečarić,, I. Perić,, and P. Vuković,, Recent Advances in Hilbert-Type Inequalities, Element, Zagreb (2012).
M. Krnić, and P. Vuković,, “Multidimensional Hilbert-type inequalities obtained via local fractional calculus,” Acta Appl. Math. (to appear).
X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Scientific Publ., New York (2012).
X. J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher, Hong Kong (2011).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 11, pp. 1454–1462, November, 2022. Ukrainian https://doi.org/10.37863/umzh.v74i11.6429.
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Vuković, P. Refinements of Local Fractional Hilbert-Type Inequalities. Ukr Math J 74, 1658–1667 (2023). https://doi.org/10.1007/s11253-023-02162-1
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DOI: https://doi.org/10.1007/s11253-023-02162-1