| Abstract: |
| A classical result due to Kenig, Ruiz and Sogge, states that the
resolvent operator for the Euclidean Laplacian (-Delta-z)^(-1) is
bounded from Lp to Lq for a certain range of indices p,q. The
operator norm depends on the frequency z, as dictated by scaling,
and it is actually independent of z for suitable values of p and q,
hence the `uniform` tag. In view of their applications to Spectral
Theory, Harmonic Analysis and Nonlinear PDEs, it is interesting to
extend these estimates to more general operators beyond the
Laplacian. In this joint work with Zhiqing Yin we consider a
general electromagnetic Laplacian and, under suitable decay
assumptions on the potentials, we recover the same range of
indices as in the free case. As an application, we deduce a
`magnetic` restriction estimate of Tomas-Stein type. |
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