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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 3, 2000, pp. 781–799
DOI: 10.4171/ZAA/980

Published online: 2000-09-30

On More General Lipschitz Spaces

Dorothee D. Haroske[1]

(1) Friedrich-Schiller-Universität Jena, Germany

The present paper deals with (logarithmic) Lipschitz spaces of type $\mathrm {Lip}^{(1,–\alpha)}_{p,q} (1 ≤ p ≤ \infty, 0 < q ≤ \infty, \alpha > \frac {1}{q})$. We study their properties and derive some (sharp) embedding results. In that sense this paper can be regarded as some continuation and extension of our papers [8, 9], but there are also connections with some recent work of Triebel concerning Hardy inequalities and sharp embeddings. Recall that the nowadays almost 'classical' forerunner of investigations of this type is the Brézis-Wainger result [6] about the 'almost' Lipschitz continuity of elements of the Sobolev spaces $H^{1+ \frac{n}{p}}_p (\mathbb R^n)$ when $1 < p < \infty$.

Keywords: Limiting embeddings, Lipschitz spaces, function spaces

Haroske Dorothee: On More General Lipschitz Spaces. Z. Anal. Anwend. 19 (2000), 781-799. doi: 10.4171/ZAA/980