4 papers
Lorentz estimates for multilinear convolution operators
Nuno J. Alves, Ana Čolović, Loukas Grafakos
We study O'Neil-type inequalities in Lorentz spaces for two extremal geometric configurations of translation-invariant multilinear convolution operators. For the one-parameter mode…
A.E. Convergence vs Boundedness
Xinyu Gao, Loukas Grafakos
We extend Stein's maximal theorem to the bilinear setting. Let be a homogeneous space with a transitive action of a compact abelian group, and let and $1/2 \l…
Uniform boundedness of parametric bilinear fractional integrals
Nuno J. Alves, Loukas Grafakos
We provide weak-type bounds for a family of bilinear fractional integrals that arise in the study of Euler-Riesz systems. These bounds are uniform in the natural parameter that des…
A bilinear fractional integral operator for Euler-Riesz systems
Nuno J. Alves, Loukas Grafakos, Athanasios E. Tzavaras
We establish a uniform estimate for a bilinear fractional integral operator via restricted weak-type endpoint estimates and Marcinkiewicz interpolation. This estimate is crucial in…