Restricted weak type on maximal linear and multilinear integral maps

Blasco, Oscar

doi:10.1090/S0002-9939-06-08798-3

Restricted weak type on maximal linear and multilinear integral maps
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Proc. Amer. Math. Soc. 135 (2007), 1343-1353 Request permission

Abstract:

It is shown that multilinear operators of the form $T(f_1,...,f_k)(x)$ $=\!\int _{\mathbb {R}^n}\!K(x,y_1,...,y_k)f_1(y_1)... f_k(y_k)dy_1...dy_k$ of restricted weak type $(1,...,1,q)$ are always of weak type $(1,...,1,q)$ whenever the map $x\to K_x$ is a locally integrable $L^1(\mathbb {R}^n)$-valued function.

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