Constructions of bounded functions related to two-sided Hardy inequalities

• Main Author: Sababheh, Mohammad Suboh.
• Format: Others
• Language: en
• Published: McGill University 2006
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102160

We investigate inequalities that can be viewed as generalizations of Hardy's inequality about the Fourier coefficients of a function analytic on the circle. The proof of the Littlewood conjecture opened a wide door in front of questions regarding possible generalizations of Hardy's inequality. The proof of the Littlewood conjecture was based on some constructions of bounded functions having particular properties. === In 1993, I. Klemes investigated one of the constructions (we shall call it the algebraic construction) and proved what is called a mixed norm generalization of Hardy's inequality. It turns out that we can work with the same construction and examine more properties of it in order to get more results. === The objectives of the thesis are to give more detailed properties of the algebraic construction and to use these properties in order to prove various versions of two-sided Hardy inequalities.