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- Larsson, Leo, 1972-
(författare)
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Carlson type inequalities and their applications
- 2003
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis treats inequalities of Carlson type, i.e. inequalities of the form∥f∥x≤K∏i=1m∥f∥Aiθiwhere ∑i=1mθi =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≤π∫0∞f2(x)dx1/4∫0∞x2 f2 (x)dx1/4first proved by F. Carlson, is the above inequality with m=2, θ1 =θ2 =1 2, X=L1(ℝ+, dx), A1 =L2 (ℝ+, dx) and A2 =L2 (ℝ+, 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.
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