Copyright © 2010 Rishad Shahmurov. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Here, we study the continuity of integral operators with operator-valued kernels. Particularly we get estimates under
some natural conditions on the kernel , where and
are Banach spaces, and
are positive measure
spaces: Then, we apply these results to extend the well-known Fourier Multiplier theorems on Besov spaces.