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Search: MSC category 26D10 ( Inequalities involving derivatives and differential and integral operators )

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1. CJM 2010 (vol 62 pp. 1116)

Jin, Yongyang; Zhang, Genkai
Degenerate p-Laplacian Operators and Hardy Type Inequalities on H-Type Groups
Let $\mathbb G$ be a step-two nilpotent group of H-type with Lie algebra $\mathfrak G=V\oplus \mathfrak t$. We define a class of vector fields $X=\{X_j\}$ on $\mathbb G$ depending on a real parameter $k\ge 1$, and we consider the corresponding $p$-Laplacian operator $L_{p,k} u= \operatorname{div}_X (|\nabla_{X} u|^{p-2} \nabla_X u)$. For $k=1$ the vector fields $X=\{X_j\}$ are the left invariant vector fields corresponding to an orthonormal basis of $V$; for $\mathbb G$ being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator $L_{p,k}$ and as an application, we get a Hardy type inequality associated with $X$.

Keywords:fundamental solutions, degenerate Laplacians, Hardy inequality, H-type groups
Categories:35H30, 26D10, 22E25

2. CJM 2000 (vol 52 pp. 920)

Evans, W. D.; Opic, B.
Real Interpolation with Logarithmic Functors and Reiteration
We present ``reiteration theorems'' with limiting values $\theta=0$ and $\theta = 1$ for a real interpolation method involving broken-logarithmic functors. The resulting spaces lie outside of the original scale of spaces and to describe them new interpolation functors are introduced. For an ordered couple of (quasi-) Banach spaces similar results were presented without proofs by Doktorskii in [D].

Keywords:real interpolation, broken-logarithmic functors, reiteration, weighted inequalities
Categories:46B70, 26D10, 46E30

3. CJM 2000 (vol 52 pp. 468)

Edmunds, D. E.; Kokilashvili, V.; Meskhi, A.
Two-Weight Estimates For Singular Integrals Defined On Spaces Of Homogeneous Type
Two-weight inequalities of strong and weak type are obtained in the context of spaces of homogeneous type. Various applications are given, in particular to Cauchy singular integrals on regular curves.

Categories:47B38, 26D10

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