Carlson type inequalities and their applications
This thesis treats inequalities of Carlson type, i.e. inequalities of the form?f?x?K?i=1m?f?Ai?iwhere ?i=1m?i =1 and K is some constant, independent of the function f. X and Ai are normed spaces, embedded in some Hausdorff topological vector space. In most cases, we have m=2, and the spaces involved are weighted Lebesgue spaces on some measure space. For example, the inequality?0?f(x)dx???0?f2(x)dx1/4?0?x2 f2 (x)dx1/4first proved by F. Carlson, is the above inequality with m=2, ?1 =?2 =1 2, X=L1(?+, dx), A1 =L2 (?+, dx) and A2 =L2 (?+, x2 dx). In different situations, suffcient, and sometimes necessary, conditions are given on the weights in order for a Carlson type inequality to hold for some constant K. Carlson type inequalities have applications to e.g. moment problems, Fourier analysis, optimal sampling, and interpolation theory.
Source Type:Doctoral Dissertation
Keywords:MATHEMATICS; Algebra, geometry and mathematical analysis; Mathematical analysis; Mathematical analysis; Carlson’s inequality; weighted inequality; Lp space; general measure space; interpolation; embedding; Matematisk analys; Mathematics; matematik
Date of Publication:01/01/2003