CRITERIA FOR THE BOUNDEDNESS AND COMPACTNESS OF INTEGRAL TRANSFORMS WITH POSITIVE KERNELS

The necessary and sufficient conditions that guarantee the boundedness and compactness of integral operators with positive kernels from $L^p(a,b)$ to $L^q_{\nu}(a,b)$, where $p,q\in(1,\infty)$ or $0lt q\leq1lt plt\infty$, for a non-negative Borel measure $\nu$ on $(a,b)$ are found.AMS 2000 Mathematics subject classification: Primary 46B50; 47B34; 47B38