We establish necessary and sufficient conditions for the one-dimensional differential Hardy inequality to hold, including the overdetermined case. The solution is given in terms different from those of the known results. Moreover, the least constant for this inequality is estimated. MSC: 26D10, 47B38.
A new discrete Hardy-type inequality with kernels and monotone functions is proved for the case 1 < q < p < ∞ . This result is discussed in a general framework and some applications related to Hölder’s summation method are pointed out. MSC: 26D10, 26D15, 39B82.