Two weight norm inequalities for fractional integral operators and commutators

Abstract

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 fractional integrals. These notes are based on three lectures delivered at the 6th International Course of Mathematical Analysis in Andalucia, held in Antequera, Spain, September 8-12, 2014. They are, however, greatly expanded to include both new results and many details that I did not present in my lectures due to time constraints.

References in corpus (4)

• The A_2 theorem: Remarks and complements
• Characterizations of BMO through commutators of bilinear singular integral operators
• A characterization of two weight trace inequalities for positive dyadic operators in the upper triangle case
• Regularity results for weak solutions of elliptic PDEs below the natural exponent

Cited by in corpus (3)

• Poincare Inequalities and Neumann Problems for the p-Laplacian
• Stein-Weiss inequality in $L^1$ norm for vector fields
• Sparse domination of weighted composition operators on weighted Bergman spaces in the upper half-plane