57 citations · 83 across the 25 of their papers we have counts for
31 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…
Nonuniform Sobolev Spaces
Ting Chen, Loukas Grafakos, Wenchang Sun
We study nonuniform Sobolev spaces, i.e., spaces of functions whose partial derivatives lie in possibly different Lebesgue spaces. Although standard proofs do not apply, we show th…
Initial bounds for multilinear operators
Loukas Grafakos, Danqing He, Petr Honzík +1
The boundedness theory of convolution operators is \linebreak based on an initial estimate derived from the Fourier transform. The corresponding theory of multil…