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Analysis of the Ahlfors-Beurling operator (lecture notes for the summer school at the University of Seville, 2013)
Oliver Dragičević
These notes are based on the ten lectures that the author held in September of 2013 at the University of Seville. The purpose of the course was to introduce basic concepts about th…
Convexity of power functions and bilinear embedding for divergence-form operators with complex coefficients
Andrea Carbonaro, Oliver Dragičević
We introduce a condition on accretive matrix functions, called -ellipticity, and discuss its applications to the theory of elliptic PDE with complex coefficients. Our exam…
Bilinear embedding for real elliptic differential operators in divergence form with potentials
Oliver Dragičević, Alexander Volberg
We present a simple Bellman function proof of a bilinear estimate for elliptic operators in divergence form with real coefficients and with nonnegative potentials. The constants ar…
Linear dimension-free estimates for the Hermite-Riesz transforms
Oliver Dragičević, Alexander Volberg
We utilize the Bellman function technique to prove a bilinear dimension-free inequality for the Hermite operator. The Bellman technique is applied here to a non-local operator, whi…