## David Cruz-Uribe

### Professor

Department Chair

- (205) 348-5074
- dcruzuribe@ua.edu
- Gordon Palmer Hall 345
- Curriculum Vitae

### Research Areas

- Analysis

### About

Professor Cruz-Uribe’s research is in harmonic analysis. He is particularly interested in the study of the classical operators of harmonic analysis—maximal operators, the Hilbert transform and other singular integrals, Riesz potentials/fractional integrals—on weighted and variable exponent Lebesgue spaces. These kinds of spaces occur naturally in situations where there is a lack of homogeneity in the underlying problem being studied. He also works on the theory of Rubio de Francia extrapolation, which allows weighted classical norm inequalities to be extended to a variety of function space settings.

Finally, he is interested in the applications of harmonic analysis to the study of partial differential equations, particularly degenerate elliptic equations.

### Selected Publications

*Variable Lebesgue Spaces and Hyperbolic Systems*, Advanced Courses in Mathematics, CRM Barcelona, Birkhauser, Basel, 2014. (Joint with A. Fiorenza, M. Ruzhansky, J. Wirth.)

*Variable Lebesgue Spaces: Foundations and Harmonic Analysis*, Birkhauser, Applied and Numerical Harmonic Analysis, 2013. (Joint with A. Fiorenza.)

*Weights, Extrapolation and the Theory of Rubio de Francia*, Operator Theory: Advances and Applications, Birkhauser, Basel, 2011. (Joint with J.M. Martell and C. Pérez.)

*Fourier Analysis*, translation and revision of the Spanish edition by Javier Duoandikoetxea, Amer. Math. Soc., Providence, December, 2000.

Photo credit: John Marinelli