No abstract uploaded!

For any interpolation pair ($A$_{0}$A$_{1}), Peetre’s$K$-functional is defined by: $$K\left( {t,a;A_0 ,A_1 } \right) = \mathop {\inf }\limits_{a = a_0 + a_1 } \left( {\left\| {a_0 } \right\|_{A_0 } + t\left\| {a_1 } \right\|_{A_1 } } \right).$$

In this paper, we characterize, for 1≤$p$<∞, the multiple ($p$, 1)-summing multilinear operators on the product of$C(K)$spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of ($p$, 1)-summing linear operators on$C(K)$in terms of their representing measures and a new multilinear characterization of$L$_{∞}spaces. We also solve a problem stated by M.S. Ramanujan and E. Schock, improve a result of H. P. Rosenthal and S. J. Szarek, and give new results about polymeasures.

No abstract uploaded!

No abstract uploaded!