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It is shown that multilinear operators of the form T(f 1 ,.., f k )(x) = f R n K(x, y1,.., y k )f 1 (y 1 )...f k (y k )dy 1 ..dy k of restricted weak type (1,...,1, q) are always of weak type (1,...,1,g) whenever the map x → K x is a locally integrable L 1 (R n )-valued function.

Restricted weak type on maximal linear and multilinear integral maps