where the constant factor [π/ sin(π/p)]p is also the best possible. Hardy-Hilbert inequalities are important in analysis and in their applications (see [7]). In recent years, many results (see [1, 3, 8–10]) have been obtained in the research of Hardy-Hilbert inequality. At present, because of the requirement of higher-dimensional harmonic analysis and higher-dimensional operator theory, multipl...

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of C. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operat...

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.