In this paper, we prove a variant of a general Hardy-Knopp type inequality. We also formulate a convolution inequality in the language of topological groups. By our main results we obtain a general form of multidimensional strengthened Hardy and Pólya-Knopp-type inequalities.

We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation. AMS subject classifications: 35P99, 35P20, 47A75, 47B25 keywords: Hardy inequality, boundary decay, Laplacian, elliptic operators, spectral theory, eigenfunctio...

A new proof is given of the atomic decomposition of Hardy spaces Hp, 0 < p ≤ 1, in the classical setting on Rn. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general and nonclassical settings.

In the early 1990s, Richard (Randy) Hardy and colleagues divided B cell precursors into subpopulations--the Hardy fractions--based on the cells' expression of various cell surface proteins. This classification helped lay the groundwork for our present-day understanding of the molecular events that control early B cell development.