The relation between Riesz potential and heat kernel on the Heisenberg group is studied. Moreover , the Hardy-Littlewood-Sobolev inequality is established.

We show that the lowest constant appearing in the weak type (1,1) inequality satisfied by the centered Hardy-Littlewood maximal operator on radial integrable functions is 1.

A Hardy inequality is established for censored stable processes on a large class of bounded domains including bounded Lipschitz domains in Rn with n ≥ 2.

In this paper, we will prove several new inequalities of Hardy type with explicit constants. The main results will be proved using generalizations of Opial's inequality.

A sharpened version of Carleman’s inequality is proved. This result unifies and generalizes some recent results of this type. Also the “ordinary” sum that serves as the upper bound is replaced by the corresponding Cesaro sum. Moreover, a Carleman type inequality with a more general measure is proved and this result may also be seen as a generalization of a continuous variant of Carleman’s inequ...

By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.

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.