Operator-valued $(L^{p},L^{q})$-Fourier multipliers

Although much of the theory of Fourier multipliers has focused on the $(L^{p},L^{p})$-boundedness

 of such operators, for many applications it suffices that a Fourier multiplier operator is bounded

 from $L^{p}$ to $L^{q}$ with p and q not necessarily equal. Moreover, one can derive 

(L^{p},L^{q})-boundedness results for $p\neq q$ under different, and often weaker, assumptions

 than in the case $p=q$. In this talk I will explain some recent results on the

 $(L^{p},L^{q})$-boundedness of operator-valued Fourier multipliers. Also, I will sketch some

 applications to the stability theory for $C_{0}$-semigroups and functional calculus theory. 

This talk will be transmitted from Warsaw to us and Dresden, provided that Warsaw get things set up.  We will not be using the TCC facility,

so the location will be C1.