Inequalities associated to Riesz potentials and non-doubling measures with applications
dc.contributor.author | Bhandari, Mukta Bahadur | |
dc.date.accessioned | 2010-08-02T21:35:04Z | |
dc.date.available | 2010-08-02T21:35:04Z | |
dc.date.graduationmonth | August | en_US |
dc.date.issued | 2010-08-02T21:35:04Z | |
dc.date.published | 2010 | en_US |
dc.description.abstract | The main focus of this work is to study the classical Calder\'{o}n-Zygmund theory and its recent developments. An attempt has been made to study some of its theory in more generality in the context of a nonhomogeneous space equipped with a measure which is not necessarily doubling. We establish a Hedberg type inequality associated to a non-doubling measure which connects two famous theorems of Harmonic Analysis-the Hardy-Littlewood-Weiner maximal theorem and the Hardy-Sobolev integral theorem. Hedberg inequalities give pointwise estimates of the Riesz potentials in terms of an appropriate maximal function. We also establish a good lambda inequality relating the distribution function of the Riesz potential and the fractional maximal function in $(\rn, d\mu)$, where $\mu$ is a positive Radon measure which is not necessarily doubling. Finally, we also derive potential inequalities as an application. | en_US |
dc.description.advisor | Charles N. Moore | en_US |
dc.description.degree | Doctor of Philosophy | en_US |
dc.description.department | Department of Mathematics | en_US |
dc.description.level | Doctoral | en_US |
dc.identifier.uri | http://hdl.handle.net/2097/4375 | |
dc.language.iso | en_US | en_US |
dc.publisher | Kansas State University | en |
dc.subject | Riesz Potentials | en_US |
dc.subject | Non-doubling Measures | en_US |
dc.subject | Good lambda inequality | en_US |
dc.subject | Hedberg Inequality | en_US |
dc.subject | Maximal Functions | en_US |
dc.subject | Weight Functions | en_US |
dc.subject.umi | Mathematics (0405) | en_US |
dc.title | Inequalities associated to Riesz potentials and non-doubling measures with applications | en_US |
dc.type | Dissertation | en_US |