A Multidimensional Cesáro Type Identity and Applications

A 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.

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.

On a Picone's identity for the $mathcal{A}_{p(x)}$-Laplacian and its applications

‎We present a Picone's identity for the‎ ‎$mathcal{A}_{p(x)}$-Laplacian‎, ‎which is an extension of the classic‎ ‎identity for the ordinary Laplace‎. ‎Also‎, ‎some applications of our‎ ‎results in Sobolev spaces with variable exponent are suggested.

Nonlinear Picone identities to Pseudo $p$-Laplace operator and applications

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

On the Cesáro Summability of Double Series