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- Alois Kufner, Lech Maligranda, Lars-Erik Persson
- The American Mathematical Monthly
- 2006

1. INTRODUCTION. The development of the famous Hardy inequality (in both its discrete and continuous forms) during the period 1906–1928 has its own history or, as we have called it, prehistory. Contributions of mathematicians other than G. are important here. In this article we describe some of those contributions. We also include and comment upon several… (More)

- Vladimir Maz’ya, Tatyana Shaposhnikova, Alois Kufner
- 2002

Abstract. Pointwise interpolation inequalities, in particular, |∇ku(x)| c (Mu(x))1−k/m (M∇mu(x)) , k < m, and |Izf(x)| c(MIζf(x)) z/Re ζ(Mf(x))1−Re z/Re ζ , 0 < Re z < Re ζ < n, where ∇k is the gradient of order k, M is the Hardy-Littlewood maximal operator, and Iz is the Riesz potential of order z, are proved. Applications to the theory of multipliers in… (More)

- Hans Triebel, Alois Kufner
- 2002

- Hans P. Heinig, Alois Kufner
- 2002

- Peter Takáč, Alois Kufner
- 2005

We investigate the smoothing effect of the parabolic part of a quasilinear evolutionary equation on its solution as time evolves. More precisely, the following initial-boundary value problem with Dirichlet boundary conditions is considered: u(x, 0) = u0(x) for x ∈ Ω. Here, ∆p stands for the negative Dirichlet p-Laplacian defined by ∆pu ≡ div(|∇u| p−2 ∇u)… (More)

- AMIRAM GOGATISHVILI, ALOIS KUFNER
- 2007

Let 1 < p ≤ q < ∞. Inspired by some recent results concerning Hardy type inequalities where the equivalence of four scales of integral conditions was proved, we use related ideas to find ten new equivalence scales of integral conditions. By applying our result to the original Hardy type inequality situation we obtain a new proof of a number of… (More)

In this paper necessary and sufficient conditions for the validity of the generalized Hardy inequality for the case −∞ < q p < 0 and 0 < p q < 1 are derived. Furthermore, some special cases are considered.

- ALOIS KUFNER, ANDREAS WANNEBO
- 2001

An interpolation inequality of Nirenberg, involving Le-besgue-space norms of functions and their derivatives, is modified, replacing one of the norms by a Hölder norm. In his paper [1], L. Nirenberg derived the inequality ∇ j u q C∇ m u a p u 1−a r (0.1) which holds for all functions u ∈ C ∞ 0 (R N) with a constant C > 0 independent of u. Here · s is the L… (More)

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