Analytic approximation inLpand coinvariant subspaces of the Hardy space

Abstract

We generalize a classical result by A. Macintyre and W. Rogosinski on best H p -approximation in L p of rational functions. For each inner function θ we give a description of H p -badly approximable functions inθH p .

Analytic balayage of measures, Carathéodory domains, and badly approximable functions in Lp

“…1.2]). The problem of describing p-badly approximable functions (in the above context as well as in certain related settings) is considered, for instance, in [1], [3], [4], [8], [13], [14], [17].…”