/pdf/the-equivalent-parameter-conditions-for-constructing-ucp0und3vv.pdf

The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications

Making use of complex analytic techniques as well as methods involving weight
 functions, we study a few equivalent conditions of a Hilbert-type integral
 inequality with nonhomogeneous kernel and parameters. In the form of
 applications we deduce a few equivalent conditions of a Hilbert-type
 integral inequality with homogeneous kernel, and we additionally consider
 operator expressions.

http://www.doiserbia.nb.rs/ft.aspx?id=1452-86302200025Y

An equivalent property of a Hilbert-type integral inequality and its applications

By means of the weight functions, the idea of introduced parameters, using the transfer formula and Hermite–Hadamard’s inequality, a more accurate half-discrete multidimensional Hilbert-type inequality with the homogeneous kernel as 1(x+||k−ξ||α)λ(x,λ>0) involving one multiple upper limit function is given, which is a new application of Hilbert-type inequalities. The equivalent conditions of the best possible constant factor related to several parameters are considered. The equivalent forms the operator expressions and some particular inequalities are obtained.

/pdf/a-more-accurate-half-discrete-multidimensional-hilbert-type-2gqcbaq0.pdf

A More Accurate Half-Discrete Multidimensional Hilbert-Type Inequality Involving One Multiple Upper Limit Function

In this paper, using weight functions as well as employing various techniques from real analysis, we establish a few equivalent conditions of two kinds of Hardy-type integral inequalities with nonhomogeneous kernel. To prove our results, we also deduce a few equivalent conditions of two kinds of Hardy-type integral inequalities with a homogeneous kernel in the form of applications. We additionally consider operator expressions. Analytic inequalities of this nature and especially the techniques involved have far reaching applications in various areas in which symmetry plays a prominent role, including aspects of physics and engineering.

https://www.mdpi.com/2073-8994/13/6/1006/pdf

Equivalent Properties of Two Kinds of Hardy-Type Integral Inequalities

In this work we establish a few equivalent statements of a Hilbert-type integral inequality in the whole plane related to the kernel of the arc tangent function. We prove that the constant factor, which is associated with the cosine function, is optimal. Some special cases as well as some operator expressions are also presented.

https://www.mdpi.com/2073-8994/13/2/351/pdf

A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function

Let Gðu, vÞ be a homogeneous nonnegative function of order λ, Kðn, kxkm,ρÞ =Gðnλ1 , kxk2 m,ρÞ. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality Ð R+ ∑n=1 Kðn, kxkm,ρÞan f ðxÞdx ≤Mk~akp,αk f kq,β are discussed. Finally, its applications in operator theory are discussed.

/pdf/equivalent-parameter-conditions-for-the-validity-of-half-1bjhaf976v.pdf

Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel

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Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel

The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications