Refinements of local fractional Hilbert-type inequalities

P.  Vuković

doi:10.37863/umzh.v74i11.6429

P. Vuković Univ. Zagreb, Croatia

DOI: https://doi.org/10.37863/umzh.v74i11.6429

Keywords: HILBERT-TYPE INEQUALITIES

Abstract

UDC 517.5

We study the re nements of several well-known local fractional Hilbert-type inequalities by interpolating the Lebesgue norms of the local fractional Laplace transforms of the functions involved in the inequalities. As an application, the main results are compared with some our results previously known from the literature.

References

Ts. Batbold, M. Krnić, P. Vuković, A unified approach to fractal Hilbert-type inequalities, J. Inequal. and Appl., 2019, Article 117 (2019). DOI: https://doi.org/10.1186/s13660-019-2076-9

Ts. Batbold, M. Krnić, J. Pečarić, 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 and Appl., 2013, (2013). DOI: https://doi.org/10.1155/2013/198405

G. H. Hardy, J. E. Littlewood, G. Pólya, Inequalities, second ed., Cambridge Univ. Press, Cambridge (1967).

G. Jumarie, Fractional Euler's integral 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, P. Vuković, Recent advances in Hilbert-type inequalities, Element, Zagreb (2012).

M. Krnić, 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 Sci. Publ., New York (2012).

X. J. Yang, Local fractional functional analysis and its applications, Asian Acad. Publ., Hong Kong (2011).