Variable exponent trace spaces

• Autorzy: Lars Diening , Peter Hästö
• Języki publikacji: EN

Abstrakty

EN

The trace space of $W^{1,p(·)}(ℝⁿ × [0,∞))$ consists of those functions on ℝⁿ that can be extended to functions of $W^{1,p(·)}(ℝⁿ × [0,∞))$ (as in the fixed-exponent case). Under the assumption that p is globally log-Hölder continuous, we show that the trace space depends only on the values of p on the boundary. In our main result we show how to define an intrinsic norm for the trace space in terms of a sharp-type operator.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 183
• Numer: 2
• Strony: 127-141

Daty

wydano

2007

Twórcy

autor

Lars Diening

• Section of Applied Mathematics, Freiburg University, Eckerstrasse 1, 79104 Freiburg/Breisgau, Germany

autor

Peter Hästö

• Department of Mathematical Sciences, P.O. Box 3000, FI-90014 University of Oulu, Finland

Identyfikatory

DOI

10.4064/sm183-2-3