Acknowledgements I would like to express my deepest appreciation to my supervisors Professor Hans-Jürgen Schmeisser and Professor Winfried Sickel for their support and many hints and comments. I thank also Professor Hans Triebel for many valuable discussions on the topic of this work.
We prove limiting imbeddings of spaces with dominating mixed derivatives into the spaces of almost Lipschitz continuous functions.
We prove dimension-free imbedding theorems for Sobolev spaces using extrapolation means and the Gross logarithmic inequality.
Our concern in this paper lies with imbeddings of general spaces of Besov and Lizorkin-Triebel type with dominating mixed derivatives in the first critical case. We employ multivariate exponential Orlicz and Lorentz-Orlicz spaces in the role of targets. We study basic properties of the target spaces, in particular, we compare them with usual exponential… (More)
Acknowledgements The organizers would like to thank the Hausdorff Center for Mathematics at the University of Bonn and the Institute of Mathematics at the University of Lübeck for the generous financial support, which made this workshop possible. In addition, they also acknowledge the support by the German Research Foundation (DFG) within the Emmy-Noether… (More)
Acknowledgements I would like to express my deepest gratitude to my supervisors Professor Hans Triebel and Professor Hans-Jürgen Schmeisser for many fruitful discussions, suggestions and remarks. I would like to thank the whole group " Function spaces " for inspiring and friendly atmosphere. Besides, I would like to thank Professor Krotov for helpful… (More)
We prove dimension-invariant imbedding theorems for Sobolev spaces using extrapolation means.