Extremality, symmetry and regularity issues in harmonic analysis

• Main Author: Carneiro, Emanuel Augusto de Souza
• Format: Others
• Language: English
• Published: 2010
• Subjects: Harmonic analysis; Sharp Strichartz inequalities; Extremal approximations; Radial symmetrization; Boltzmann collision operator; Convolution inequalities; Maximal operators regularity
• Online Access: http://hdl.handle.net/2152/7474

In this Ph. D. thesis we discuss four different problems in analysis: (a) sharp inequalities related to the restriction phenomena for the Fourier transform, with emphasis on some Strichartz-type estimates; (b) extremal approximations of exponential type for the Gaussian and for a class of even functions, with applications to analytic number theory; (c) radial symmetrization approach to convolution-like inequalities for the Boltzmann collision operator; (d) regularity of maximal operators with respect to weak derivatives and weak continuity. === text