Bellman Functions on Simple Non-Convex Domains in the Plane

Beschreibung

This memoir provides a generalization of the authors' previous work on Bellman functions for integral functionals on \mathrm{BMO}. Those Bellman functions are the minimal locally concave functions on parabolic strips in the plane. We describe an algorithm for constructing minimal locally concave functions on a planar domain that is a difference of two unbounded convex domains. This leads to many sharp estimates for functions in the classes like \mathrm{BMO}, A_p, or the Gehring classes.

Autor*in

Paata Ivanisvili
University of California, Irvine, USA

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Bellman function extremal problems sharp inequalities bounded mean oscillation Muckenhoupt classes Gehring classes

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