Some new Stein and Hardy type inequalities (Q548727)

The authors prove some new generalizations of two Hardy type inequalities, by considering two multidimensional Hardy-Littlewood type oerators with nonnegative kernels, satisfying certain conditions. The results are consequences of pointwise Stein type inequalities which, together with known results for the maximal operator imply new results concerning multidimensional Hardy inequalities even in the case of variable \(L^{p(.)}\) spaces. The theorems are however, too complicated to be stated here. The list of references contains a number of 40 items.