معرفی
David Cruz-Uribe is a Professor in the Department of Mathematics at the University of Alabama. His research focuses on harmonic analysis, with emphasis on weighted and variable exponent Lebesgue spaces, extrapolation theory, and applications to partial differential equations, particularly degenerate elliptic equations. He has authored/co-authored multiple books, including The Stieltjes Integral (2023) and Variable Lebesgue Spaces: Foundations and Harmonic Analysis (2013). His work bridges abstract harmonic analysis with practical applications in PDEs, contributing to the understanding of maximal operators, singular integrals, and fractional operators in nonhomogeneous spaces.
His research interests include the study of classical harmonic analysis operators (maximal functions, Hilbert transform, fractional integrals) on weighted spaces, and their role in solving degenerate elliptic and parabolic equations. He also explores the interplay between weighted norm inequalities and functional spaces like Orlicz and variable exponent spaces.
Key contributions include advancements in the theory of Rubio de Francia extrapolation, reverse Hölder inequalities for matrix weights, and the development of modular inequalities in variable Lebesgue spaces. These tools underpin his work on PDEs, where he addresses regularity of solutions and existence under non-standard conditions.
He has secured grants such as the RUI: Harmonic Analysis on Weighted Lebesgue Spaces (2014). His publications span over two decades, reflecting sustained innovation in his field. While no specific awards are listed, his extensive publication record and authorship of foundational texts highlight his scholarly impact.
