Critical Numbers and \(\mathrm {L}^p\mbox{--}\mathrm {L}^q\) Bounded Families of Operators

So far, we studied elliptic systems merely on the space \(\mathrm {L}^2\) . This is going to change now. More precisely, we are interested to which \(\mathrm {L}^p\) spaces an operator like \((1+t^2 L)^{-1}\) , initially defined only on \(\mathrm {L}^2\) , extends by continuity.