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Applications of the Bellman Function Technique in Multilinear and Nonlinear Harmonic Analysis (CROSBI ID 365537)

Ocjenski rad | doktorska disertacija

Kovač, Vjekoslav Applications of the Bellman Function Technique in Multilinear and Nonlinear Harmonic Analysis / Thiele, Christoph (mentor); Los Angeles, . 2011

Podaci o odgovornosti

Kovač, Vjekoslav

Thiele, Christoph

engleski

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

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".

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

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Podaci o izdanju

110

18.08.2011.

obranjeno

Podaci o ustanovi koja je dodijelila akademski stupanj

Los Angeles

Povezanost rada

Matematika