Constructions of bounded functions related to two-sided Hardy inequalities
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 inequal...
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| Format: | Others |
| Language: | en |
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McGill University
2006
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| Online Access: | http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102160 |
| Summary: | 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. |
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