|
In this seminar we study the traces of 2-microlocal Triebel-Lizorkin spaces with variable integrability on hyperplanes. Following [2], we present the definition and properties of those spaces, in particular the characterization by atomic decomposition and embedding assertions, needed to prove the trace result. We emphasize that the function spaces considered cover Triebel-Lizorkin spaces with variable smoothness and variable integrability as well as weighted Triebel-Lizorkin spaces. The trace result to be proved extends the one obtained in [1] and is the counterpart for Triebel-Lizorkin spaces of the one obtained in [3] for Besov type spaces. References
[1] L. Diening, P. Hasto, and S. Roudenko, Function spaces of variable smoothness and integrability, J. Funct. Anal. 256 (2009), no. 6, 1731-1768.
[2] H. Kempka, Atomic, molecular and wavelet decomposition of 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability, Funct. Approx. Comment. Math. 43 (2010), no. 2, 171-208.
[3] S. D. Moura, J. S. Neves, and C. Schneider, On trace spaces of 2-microlocal Besov spaces with variable integrability, Math. Nachr., 2013, online.
|
