Naslov
Multilinear singular integrals associated with hypergraphs

Autori
Stipčić, Mario

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Mjesto
Zagreb

Datum
14.12

Godina
2020

Stranica
121

Mentor
Kovač, Vjekoslav

Ključne riječi
hypergraph, singular integral forms, entangled multilinear singular integral forms, T(1)-type conditions, ergodic-martingale paraproduct, Kakutani’s question, Lp estimates, removal lemmas

Sažetak
This work contributes to the theory of entangled multilinear singular integral forms by giving the first characterizations of Lp boundedness of dyadic versions of these forms associated with hypergraphs. Moreover, it establishes the first weighted estimates and sparse domination results for such forms. The work proceeds by applying the obtained characterizations to an open problem in probability theory. It introduces the notion of ergodic-martingale paraproducts and establishes their boundedness and convergence in a certain range of the Lp norms. This gives a possible answer to a classical question by Kakutani. Finally, the work discusses connections with the removal lemmas from arithmetic combinatorics and graph theory.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA