Naslov
Applications of the Bellman Function Technique in Multilinear and Nonlinear Harmonic Analysis

Autori
Kovač, Vjekoslav

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
UCLA, Department of Mathematics

Mjesto
Los Angeles

Datum
18.08

Godina
2011

Stranica
110

Mentor
Thiele, Christoph

Ključne riječi
paraproduct ; bilinear multiplier ; multilinear operator ; scattering transform ; Bellman function ; Cantor group

Sažetak
Large part of this work is motivated by a question raised by Demeter and Thiele on establishing L^p estimates for a two-dimensional bilinear operator of paraproduct type, called the "twisted paraproduct". We confirm this conjecture by proving estimates in a certain range of exponents. As a byproduct of the approach we develop a rather general technique for verifying multilinear estimates. This method is subsequently further applied to show L^p bounds for a class of two-dimensional multilinear forms that generalize (dyadic variants of) both classical paraproducts and the twisted paraproduct. The remaining material is related to the one-dimensional Dirac scattering transform. Muscalu, Tao, and Thiele asked if the analogues of Hausdorff-Young inequalities are valid with constants independent of p. We provide positive answer to this question in the case where the exponentials are replaced by the character function of the "d-adic model" of the real line. Our main tool for all of the attempted problems, both multilinear and nonlinear in nature, is the Bellman function technique, briefly described as "systematic induction over scales".

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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