Hilbert Inequalities Research Articles

Gamma-Nabla Hardy–Hilbert-Type Inequalities on Time Scales

We investigated several novel conformable fractional gamma-nabla dynamic Hardy–Hilbert inequalities on time scales in this study. Several continuous inequalities and their corresponding discrete analogues in the literature are combined and expanded by these inequalities. Hölder’s inequality on time scales and a few algebraic inequalities are used to demonstrate our findings.

Important Study on the ∇ Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert-type on time scales. We present and prove very important generalized results with the help of the Fenchel–Legendre transform, submultiplicative functions, and Hölder’s and Jensen’s inequality on time scales. We obtain some well-known time scale inequalities due to Hardy–Hilbert inequalities. For some specific time scales, we further show some relevant inequalities as special cases: integral inequalities and discrete inequalities. Symmetry plays an essential role in determining the correct methods for solutions to dynamic inequalities

Calderón Operator on Local Morrey Spaces with Variable Exponents

In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of the local Morrey spaces with the exponent functions are only required to satisfy the log-Hölder continuity assumption at the origin and infinity only. As special cases of the main result, we have Hardy’s inequalities, the Hilbert inequalities and the boundedness of the Riemann–Liouville and Weyl averaging operators on local Morrey spaces with variable exponents.

Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert type on time scales. We present and prove very important generalized results with the help of Fenchel–Legendre transform, submultiplicative functions. We prove the (γ,a)-nabla conformable Hölder’s and Jensen’s inequality on time scales. We prove several inequalities due to Hardy–Hilbert inequalities on time scales. Furthermore, we introduce the continuous inequalities and discrete inequalities as special case.

On finite sections of the multiplicative Hilbert inequalities

AbstractWe determine the asymptotic behavior of the eigenvalues of finite sections of the multiplicative Hilbert matrices.

Dilation operators and integral operators on amalgam space $$(L_{p},l_{q})$$(Lp,lq)

This paper establishes the Hardy–Littlewood–Polya inequalities, the Hardy inequalities and the Hilbert inequalities on amalgam spaces. Moreover, it also gives the mapping properties of the Mellin convolutions, the Hadamard fractional integrals and the Hausdorff operators on amalgam spaces. We establish these properties by some estimates for the operator norms of the dilation operators on amalgam spaces.

Reverse Hilbert inequalities involving series

Some reverse Hilbert's type inequalities involving series of nonnegative terms are established by the use of the technique of real analysis, which provides new estimates on inequalities of these type.

More Accurate Hilbert-Type Inequalities in a Difference Form

In the present paper we establish several more accurate Hilbert-type inequalities in a difference form. Our main results rely on some recent improvements of the Young inequality. First, we give refinements and reverses of the Holder inequality. Then, by virtue of the improved Holder inequality, we give two classes of refinements and reverses for general Hilbert-type inequalities. As an application, we give strengthened forms of the classical Hilbert and Hardy inequalities.

New half-discrete Hilbert inequalities for three variables

In this paper, we obtain two new half-discrete Hilbert inequalities for three variables. The obtained inequalities are with the best constant factor. Moreover, we give their equivalent forms.

On Hilbert's inequalities with alternating signs

On Hilbert's inequalities with alternating signs

A Class of Hilbert-Type Inequalities Obtained Via the Improved Young Inequality

In this article we establish a class of more accurate Hilbert-type inequalities based on an improved form of the Young inequality, known from the literature. We obtain refined and reversed relations in a general multidimensional case. As an application, we give improved versions of the classical Hilbert and Hardy inequalities.

Reverse Hilbert's type integral inequalities

In this paper, we are motivated by some newer Hilbert-Pachpatte inequalities, and that we derive some similar (but reverse) inequalities. Mathematics subject classification (2010): 26D15.

Multiple Hilbert's type inequalities with a homogeneous kernel

The main objective of this paper is a study of some new generalizations of Hilbert's and Hardy-Hilbert's type inequalities. We apply our general results to homogeneous functions. Also, we obtain the best possible constants when the parameters satisfy appropriate conditions.

GENERALIZED NONCOMMUTATIVE HARDY AND HARDY–HILBERT TYPE INEQUALITIES

We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy–Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.

Hardy-Hilbert-Type Inequalities with a Homogeneous Kernel in Discrete Case

The main objective of this paper is a study of some new generalizations of Hilbert's and Hardy-Hilbert's type inequalities. We apply our general results to homogeneous functions. We shall obtain, in a similar way as Yang did in(2009), that the constant factors are the best possible when the parameters satisfy appropriate conditions.

Some New Hilbert's Type Inequalities

Some new inequalities similar to Hilbert's type inequality involving series of nonnegative terms are established.

On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters

By introducing some parameters and a norm |x|α , x ∈ R+ , we give higherdimensional Hilbert’s and Hardy-Hilbert’s integral inequalities in non-conjugate case. Further, we prove that their constant factors are the best possible, in the conjugate case, when the parameters satisfy appropriate conditions. We also compare our results with some known results. Mathematics subject classification (2000): 26D15.

On Inverse Hilbert-Type Inequalities

This paper deals with new inverse-type Hilbert inequalities. Our results in special cases yield some of the recent results and provide some new estimates on such types of inequalities.

Some remarks on reverse Hilbert and Hardy-Hilbert type inequalities

In this paper we obtain an extension of discrete Hilbert’s inequality, by using some numerical methods. We shall obtain, in a similar way as Yang did in [10], that the parameter from the kernel can be taken from the interval [3/2, 3). We also compare our findings with existing results, known from the literature.

On Hilbert's type inequalities

By introducing two pairs of conjugate exponents and estimating the weight coefficients, we give generalizations of some Hilbert's type inequalities with the best constant factor. As applications, some particular results are considered.