WIAS Preprint No. 1972, (2014)

Reverse inequalities for slowly increasing sequences and functions



Authors

  • Stephan, Holger

2010 Mathematics Subject Classification

  • 26D15 35A23

Keywords

  • reverse inequalities, slowly increasing sequences, slowly increasing functions

Abstract

We consider sharp inequalities involving slowly increasing sequences and functions, i.e., functions $f(t)$ with $f'(t) leq 1$ and sequences $(a_i)$ with $a_i+1-a_i leq 1$. The inequalities are reverse to mean inequalities, for example. In the continuous case, integrals of powers are estimated by powers of integrals, whereas in the discrete case powers of sums are estimated by sums of powers of sums. The problem is connected with interpolation theory in Banach spaces, one of them $W^1,infty$.

Appeared in

  • Octogone Math. Mag., 22 (2015) pp. 621--633.

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