On a Multidimensional Hilbert–type Integral Inequality with Logarithm Function
نویسندگان
چکیده
By the use of the transfer formula, the methods of weight functions and technique of Real Analysis, a multidimensional Hilbert-type integral inequality with a few parameters and a best possible constant factor related to the kernel of logarithm function is given. The equivalent forms and some reverses are obtained. The operator expressions and a few particular results related to the kernels of non-homogeneous and homogeneous are considered. Mathematics subject classification (2010): 26D15, 47A07, 37A10.
منابع مشابه
An extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel
In this paper, by the use of the weight coefficients, the transfer formula and the technique of real analysis, an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions and a few examples are considered.
متن کاملA multidimensional discrete Hilbert-type inequality
In this paper, by using the way of weight coecients and technique of real analysis, a multidimensionaldiscrete Hilbert-type inequality with a best possible constant factor is given. The equivalentform, the operator expression with the norm are considered.
متن کاملOn a decomposition of Hardy--Hilbert's type inequality
In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.
متن کاملA more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function
By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...
متن کاملGeneral Hardy-Type Inequalities with Non-conjugate Exponents
We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015