Multidimensional Hilbert-Type Inequalities Obtained via Local Fractional Calculus

被引：0
作者：
Mario Krnić
Predrag Vuković
机构：
[1] University of Zagreb,Faculty of Electrical Engineering and Computing
[2] University of Zagreb,Faculty of Teacher Education
来源：
Acta Applicandae Mathematicae | 2020年 / 169卷
关键词：
Hilbert inequality; Conjugate parameters; Homogeneous function; Local fractional calculus; Multidimensional form; 26D15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we give a unified treatment of multidimensional fractal Hilbert-type inequalities. More precisely, we establish a Hilbert-type inequality with a general local fractional continuous kernel and weight functions. A particular emphasis is dedicated to a class of inequalities with a homogeneous kernel. Namely, we impose some weak conditions for which the constants appearing on the right-hand sides of such Hilbert-type inequalities are the best possible. As an application, we discuss some particular choices of homogeneous kernels and power weight functions.
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页码：667 / 680
页数：13
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共 32 条
[1]  
Adiyasuren V.(2016)Multiple Hilbert-type inequalities involving some differential operators Banach J. Math. Anal. 10 320-337
[2]  
Batbold Ts.(2018)A further extension of Mittag-Leffler function Fract. Calc. Appl. Anal. 21 1377-1395
[3]  
Krnić M.(2018)New aspects of Opial-type integral inequalities J. Inequal. Appl. 2018 625-658
[4]  
Andrić M.(2018)Hardy-type inequalities within fractional derivatives without singular kernel J. Inequal. Appl. 2018 257-273
[5]  
Farid G.(2019)A unified approach to fractal Hilbert-type inequalities J. Inequal. Appl. 2019 185-196
[6]  
Pečarić J.(2003)On the way of weight coefficients and research for the Hilbert-type inequalities Math. Inequal. Appl. 6 729-737
[7]  
Basci Y.(2010)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. 28 772-780
[8]  
Baleanu D.(2017)A class of Hilbert-type inequalities obtained via the improved Young inequality Results Math. 71 408-418
[9]  
Basci Y.(2018)A Hilbert-type fractional integral inequality with the kernel of Mittag-Leffler function and its applications Math. Inequal. Appl. 21 1527-1538
[10]  
Baleanu D.(2017)A Hilbert-type integral inequality on the fractal spaces Integral Transforms Spec. Funct. 28 316-323
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