Multilinear paraproducts revisited

Abstract

We prove that multilinear paraproducts are bounded from products of Lebesgue spaces L^{p_1}\!\times \cdots \times L^{p_{m+1}} to L^{p,\infty} , when 1\le\! p_1, \dots , p_m , p_{m+1}<\infty , 1/p_1+\cdots +1/p_{m+1}=1/p . We focus on the endpoint case when some indices p_j are equal to 1 , in particular we obtain a new proof of the estimate L^1\times \cdots \times L^1\to L^{1/(m+1),\infty} .

Locations

• Revista Matemática Iberoamericana - View - PDF