Lipschitz continuity in Muckenhoupt $\mathcal{A}_1$ weighted function spaces

Volume 92 / 2011

Dorothee D. Haroske Banach Center Publications 92 (2011), 107-129 MSC: Primary 46E35; Secondary 42B35, 47B06. DOI: 10.4064/bc92-0-8


We study continuity envelopes of function spaces $\newcommand{\rn}{{\mathbb{R}^n}}\newcommand{\B}{{B^s_{p,q}}}\B(\rn,w)$ and $\newcommand{\rn}{{\mathbb{R}^n}}\newcommand{\F}{{F^s_{p,q}}}\F(\rn,w)$ where the weight belongs to the Muckenhoupt class $\mathcal{A}_1$. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.


  • Dorothee D. HaroskeMathematical Institute
    Friedrich-Schiller-University Jena
    D-07737 Jena, Germany

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