scholarly journals A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY IN THE WHOLE PLANE

2017 ◽  
Vol 7 (3) ◽  
pp. 977-991
Author(s):  
Bicheng Yang ◽  
◽  
Bing He
Keyword(s):  
Type Inequality ◽  
Hilbert Type

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.

scholarly journals INEQUALITIES OF THE HILBERT TYPE IN $\mathbb{R}^{n}$ WITH NON-CONJUGATE EXPONENTS

2008 ◽  
Vol 51 (1) ◽  
pp. 11-26
Author(s):  
Aleksandra Čižmešija ◽  
Ivan Perić ◽  
Predrag Vuković
Keyword(s):  
Sobolev Inequality ◽  
Integral Formula ◽  
Type Inequality ◽  
Upper Bounds ◽  
Conjugate Exponents ◽  
Hilbert Type

AbstractIn this paper we state and prove a new general Hilbert-type inequality in $\mathbb{R}^{n}$ with $k\geq2$ non-conjugate exponents. Using Selberg's integral formula, this result is then applied to obtain explicit upper bounds for the doubly weighted Hardy–Littlewood–Sobolev inequality and some further Hilbert-type inequalities for $k$ non-negative functions and non-conjugate exponents.

scholarly journals A New Hilbert-Type Inequality with Positive Homogeneous Kernel and Its Equivalent Forms

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 342 ◽  
Author(s):  
Bicheng Yang ◽  
Shanhe Wu ◽  
Aizhen Wang
Keyword(s):  
Type Inequality ◽  
Homogeneous Kernel ◽  
Hilbert Type

We establish a new inequality of Hilbert-type containing positive homogeneous kernel ( min { m , n } ) λ and derive its equivalent forms. Based on the obtained Hilbert-type inequality, we discuss its equivalent forms and give the operator expressions in some particular cases.

scholarly journals On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 229 ◽  
Author(s):  
Jianquan Liao ◽  
Shanhe Wu ◽  
Bicheng Yang
Keyword(s):  
Type Inequality ◽  
Constant Factor ◽  
Partial Sums ◽  
Upper Limit ◽  
The Best Possible Constant ◽  
Special Case ◽  
Equivalent Conditions ◽  
Hilbert Type

In this paper we establish a new half-discrete Hilbert-type inequality involving the variable upper limit integral and partial sums. As applications, an inequality obtained from the special case of the half-discrete Hilbert-type inequality is further investigated; moreover, the equivalent conditions of the best possible constant factor related to several parameters are proved.

scholarly journals A Half-Discrete Hilbert-Type Inequality in the Whole Plane with Multiparameters

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Qunwei Ma ◽  
Bicheng Yang ◽  
Leping He
Keyword(s):  
Type Inequality ◽  
Constant Factor ◽  
Weight Functions ◽  
Real Analysis ◽  
The Best Possible Constant ◽  
Hilbert Type

By the use of weight functions and technique of real analysis, a new half-discrete Hilbert-type inequality in the whole plane with multiparameters and the best possible constant factor is given. Furthermore, the equivalent forms, two kinds of particular inequalities, and the operator expressions with the norm are considered.

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