Weighted mixed weak-type inequalities for multilinear fractional operators


  • M. Belén Picardi Instituto de Matemática (INMABB), Departamento de Matemática, Universidad Nacional del Sur (UNS)-CONICET, Bahía Blanca, Argentina




The aim of this paper is to obtain mixed weak-type inequalities for multilinear fractional operators, extending results by Berra, Carena and Pradolini [Math. Anal. Appl. 479 (2019)]. We prove that, under certain conditions on the weights, there exists a constant $C$ such that \[ \Bigg\| \frac{\mathcal{G}_{\alpha}(\vec{f}\,)}{v}\Bigg\|_{L^{q, \infty}(\nu v^q)} \leq C \prod_{i=1}^m{\|f_i\|_{L^1(u_i)}}, \] where $\mathcal{G}_{\alpha}(\vec{f}\,)$ is the multilinear maximal function $\mathcal{M}_{\alpha}(\vec{f}\,)$ introduced by Moen [Collect. Math. 60 (2009)] or the multilineal fractional integral $\mathcal{I}_{\alpha}(\vec{f}\,)$. As an application, a vector-valued weighted mixed inequality for $\mathcal{I}_{\alpha}(\vec{f}\,)$ is provided.


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