I wrote my Master Thesis on Sparse Domination, a technique in Harmonic Analysis where Sparse Operators are used to prove weighted bounds for varied classes of operators. The main benefit of these operators is that they allow us to keep track of the dependence of these bounds on the Ap characteristic of the weight, in many cases yielding results known to be sharp. This technique originated from a sequence of simplifications to the proof of the A2 conjecture and was later generalized to many other settings, proving new results in these contexts. The thesis starts with an overview of Ap weights, then contains the proof of the A2 conjecture via Sparse Domination (first motivated by the toy example of the Maximal Dyadic Operator) and finally contains some examples and references to generalizations of the technique.
