Maximization of functionals in $H^\omega [a,b]$

S. K. Bagdasarov

Sbornik. Mathematics, Tome 189 (1998) no. 2, pp. 159-226

Résumé

The structure and the properties of the extremal functions in the problem $$ \int _a^b h(t)\psi (t)\,dt\to \sup, \qquad h\in H^\omega [a,b], $$ are described in the case when $\psi$ is an integrable function with zero mean and finitely many points of sign change on $[a,b]$ and $H^\omega [a,b]$ is the class of absolutely integrable functions on $[a,b]$ with modulus of continuity majorized by a fixed convex modulus of continuity $\omega$.