Abstract
We consider Hörmander type spectral multiplier problem for Schrödinger operator with a critical potential in one and three dimensions. It is shown that the multiplier operator is bounded on Lp, Besov spaces and Triebel-Lizorkin spaces under the same sharp condition. We then derive Strichartz estimates for the corresponding wave equations.
Our work is partially motivated by the standing wave problem for the quintic wave equation in 3+1 spacetime dimensions.
Original language | American English |
---|---|
State | Published - Apr 1 2009 |
Event | University of South Wales Analysis Seminar - Syndey, New South Wales, Australia Duration: Apr 1 2009 → … |
Conference
Conference | University of South Wales Analysis Seminar |
---|---|
Period | 04/1/09 → … |
Disciplines
- Mathematics
Keywords
- Hoermander type spectral multiplier problem
- Schroedinger operators
- Triebel-Lizorkin spaces