JournalszaaVol. 19 , No. 3pp. 781–799

On More General Lipschitz Spaces

  • Dorothee D. Haroske

    Friedrich-Schiller-Universität Jena, Germany
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The present paper deals with (logarithmic) Lipschitz spaces of type Lipp,q(1,α)(1p,0<q,α>1q)\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 Hp1+np(Rn)H^{1+ \frac{n}{p}}_p (\mathbb R^n) when 1<p<1 < p < \infty.

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Dorothee D. Haroske, On More General Lipschitz Spaces. Z. Anal. Anwend. 19 (2000), no. 3 pp. 781–799

DOI 10.4171/ZAA/980