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Two weight norm inequalities for fractional integral operators and commutators
David Cruz-Uribe
In these lecture notes we describe some recent work on two weight norm inequalities for fractional integral operators, also known as Riesz potentials, and for commutators of fracti…
Greedy bases in variable Lebesgue spaces
David Cruz-Uribe, SFO, Eugenio Hernández +1
We compute the right and left democracy functions of admissible wavelet bases in variable Lebesgue spaces defined on . As an application we give Lebesgue type inequalities for…
Extrapolation and weighted norm inequalities in the variable Lebesgue spaces
David Cruz-Uribe, Li-An Daniel Wang
We extend the theory of Rubio de Francia extrapolation, including off-diagonal, limited range, and extrapolation, to the weighted variable Lebesgue spaces. As a conseq…
Regularity results for weak solutions of elliptic PDEs below the natural exponent
David Cruz-Uribe, Kabe Moen, Scott Rodney
We prove regularity estimates for weak solutions to the Dirichlet problem for a divergence form elliptic operator. We give estimates for the second derivative for . Our…