Optimal domains for kernel operators on $[0,\infty )\times [0,\infty )$
Volume 174 / 2006
Studia Mathematica 174 (2006), 131-145
MSC: Primary 47B38, 46E30; Secondary 47G10, 46G10.
DOI: 10.4064/sm174-2-2
Abstract
Let $T$ be a kernel operator with values in a rearrangement invariant Banach function space $X$ on $[0,\infty )$ and defined over simple functions on $[0,\infty )$ of bounded support. We identify the optimal domain for $T$ (still with values in $X$) in terms of interpolation spaces, under appropriate conditions on the kernel and the space $X$. The techniques used are based on the relation between linear operators and vector measures.
