On a strengthened multidimensional Hilbert-type inequality

2014 ◽  
Vol 64 (5) ◽  
Author(s):  
Mario Krnić
Keyword(s):  
Hölder’S Inequality ◽  
Type Inequality ◽  
Hölder's Inequality ◽  
Weighted Functions ◽  
Hilbert Type

AbstractThe main objective of this paper is a study of the general refinement and converse of the multidimensional Hilbert-type inequality in the so-called quotient form. Such extensions are deduced with the help of the sophisticated use of the well-known Hölder’s inequality. The obtained results are then applied to homogeneous kernels with the negative degree of homogeneity. Also, we establish the conditions under which the constant factors involved in the established inequalities are the best possible. Finally, we consider some particular settings with homogeneous kernels and weighted functions. In such a way we obtain both refinements and converses of some actual results, known from the literature.

scholarly journals Hilbert-type inequalities for time scale nabla calculus

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
H. M. Rezk ◽  
Ghada AlNemer ◽  
H. A. Abd El-Hamid ◽  
Abdel-Haleem Abdel-Aty ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Time Scale ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Arbitrary Time ◽  
Hilbert Type

Abstract This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.

scholarly journals A New Reversed Version of a Generalized Sharp Hölder's Inequality and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jingfeng Tian ◽  
Xi-Mei Hu
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Type Inequality ◽  
Hölder's Inequality

We present a new reversed version of a generalized sharp Hölder's inequality which is due to Wu and then give a new refinement of Hölder's inequality. Moreover, the obtained result is used to improve the well-known Popoviciu-Vasić inequality. Finally, we establish the time scales version of Beckenbach-type inequality.

scholarly journals Some Dynamic Inequalities of Hilbert’s Type

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
A. M. Ahmed ◽  
Ghada AlNemer ◽  
M. Zakarya ◽  
H. M. Rezk
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Hölder's Inequality ◽  
Discrete Inequalities ◽  
Special Case ◽  
Hilbert Type

This paper is concerned with deriving some new dynamic Hilbert-type inequalities on time scales. The basic idea in proving the results is using some algebraic inequalities, Hölder’s inequality and Jensen’s inequality, on time scales. As a special case of our results, we will obtain some integrals and their corresponding discrete inequalities of Hilbert’s type.

scholarly journals A New Refinement of Generalized Hölder’s Inequality and Its Application

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jingfeng Tian
Keyword(s):  
Hölder’S Inequality ◽  
Type Inequality ◽  
Hölder's Inequality

We present a new refinement of generalized Hölder’s inequality due to Vasić and Pečarić. Moreover, the obtained result is used to improve Beckenbach-type inequality due to Wang.

scholarly journals ON SOME REFINEMENTS AND CONVERSES OF MULTIDIMENSIONAL HILBERT-TYPE INEQUALITIES

2012 ◽  
Vol 85 (3) ◽  
pp. 380-394 ◽  
Author(s):  
MARIO KRNIĆ
Keyword(s):  
Type Inequality ◽  
Hölder Inequality ◽  
Weighted Functions ◽  
Difference Form ◽  
Hilbert Type

AbstractThe main objective of this paper is a study of some new refinements and converses of multidimensional Hilbert-type inequalities with nonconjugate exponents. Such extensions are deduced with the help of some remarkable improvements of the well-known Hölder inequality. First, we obtain refinements and converses of the general multidimensional Hilbert-type inequality in both quotient and difference form. We then apply the results to homogeneous kernels with negative degree of homogeneity. Finally, we consider some particular settings with homogeneous kernels and weighted functions, and compare our results with those in the literature.

scholarly journals On a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xingshou Huang ◽  
Bicheng Yang
Keyword(s):  
Equivalent Form ◽  
Type Inequality ◽  
Constant Factor ◽  
Real Analysis ◽  
Homogeneous Kernel ◽  
Hilbert’S Inequality ◽  
The Best Possible Constant ◽  
Hilbert Type ◽  
Weight Coefficients

AbstractBy the use of the weight coefficients, the idea of introduced parameters and the technique of real analysis, a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel is given, which is an extension of the more accurate Hardy–Hilbert’s inequality. An equivalent form is obtained. The equivalent statements of the best possible constant factor related to several parameters, the operator expressions and a few particular cases are considered.

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