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.
Both authors were partially supported by DGICYT grant BMF2001-1284.
"Multiple summing operators on C(K) spaces." Ark. Mat. 42 (1) 153 - 171, April 2004. https://doi.org/10.1007/BF02432914