We consider the question of the density in the space Lp, 1 ≤ p ≤ ∞, on the unit circle, of the subspaces Hp+σmk=1 wkHp, where Hp is the standard Hardy space and w1,...,wm are given functions in the class L∞. This question is closely related to problems of uniform and Lp-approximations of functions by polyanalytic polynomials on the boundaries of simple connected domains in ℂ. The obtained results are formulated in terms of Nevanlinna and d-Nevanlinna domains, that is, in terms of special analytic characteristics of simply connected domains in ℂ, which are related to the pseudocontinuation property of bounded holomorphic functions
Original language | English |
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Pages (from-to) | 140-154 |
Number of pages | 15 |
Journal | Sbornik Mathematics |
Volume | 207 |
Issue number | 1 |
DOIs | |
State | Published - 2016 |
Externally published | Yes |
ID: 86669439