Weight characterizations of discrete Hardy and Carleman type inequalities
Abstract (Summary)This thesis deals with some generalizations of the discrete Hardy and Carleman type inequalities and the relations between them. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In particular, a fairly complete description of the development of discrete Hardy and Carleman type inequalities in one and more dimensions can be found in this chapter. In Chapter 2 we consider some scales of weight characterizations for the one-dimensional discrete Hardy inequality for the case 1In Chapter 3 we present and discuss a new scale of weight characterizations for a two-dimensional discrete Hardy type inequality and its limit two-dimensional Carleman type inequality. In Chapter 4 we generalize the work done in Chapters 2 and 3 and present, prove and discuss the corresponding general n-dimensional versions. In Chapter 5 we introduce the study of the general Hardy type inequality with kernels involved. For kernels of product type a weight characterization is given, thus generalizing a previous result of M. Goldman. A scale of sufficient conditions is proved for the general case. Finally, in the Appendix some steps in the historical development of the continuous Hardy inequality are briefly described.
School:Luleå tekniska universitet
Source Type:Master's Thesis
Date of Publication:01/01/2005