2005:45|issn: 1402-1757|isrn: ltu-lic-- 05 ⁄45-- seWeight Characterizations of Discrete Hardy and Carleman Type Inequalities

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 1 <p ≤ q<∞. These characterizations contain a parameter s and as endpoint results we obtain the usual characterizations of Muckenhoupt or Bennett type. As limit cases some weight characterizations of Carleman type inequalities are obtained for the case 0 <p ≤ q<∞. In 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 n

Weight characterizations for the discrete Hardy inequality with kernel

A discrete Hardy-type inequality is considered for a positive &#147;kernel&#148; , , and . For kernels of product type some scales of weight characterizations of the inequality are proved with the corresponding estimates of the best constant . A sufficient condition for the inequality to hold in the general case is proved and this condition is necessary in special cases. Moreover, some corresponding results for the case when are replaced by the nonincreasing sequences are proved and discussed in the light of some other recent results of this type.</p