Geodesic
Whitney decomposition, embedding theorems, and interpolation in weighted spaces of analytic functions
Vladikavkazskij matematičeskij žurnal, Tome 21 (2019) no. 1, pp. 62-73 
F. A. Shamoyan; E. V. Tasoeva. Whitney decomposition, embedding theorems, and interpolation in weighted spaces of analytic functions. Vladikavkazskij matematičeskij žurnal, Tome 21 (2019) no. 1, pp. 62-73. http://geodesic.mathdoc.fr/item/VMJ_2019_21_1_a5/
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     author = {F. A. Shamoyan and E. V. Tasoeva},
     title = {Whitney decomposition, embedding theorems, and interpolation in weighted spaces of analytic functions},
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     url = {http://geodesic.mathdoc.fr/item/VMJ_2019_21_1_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

According to the classical Whitney theorem, each open set on the plane can be decomposed as a union of special squares whose interiors do not intersect. In the paper, using the properties of Whitney squares, a new concept is introduced. For each center $a_k$ of the Whitney square, there is a point $a_k^*\in \mathbb{C}\setminus G$ such that the distance to the boundary of the open set $G$ is between two constants, regardless of $k$. In particular, a necessary and sufficient condition for a sequence $(z_k)_1^{\infty}\subset G$ under which the operator $R(f)=(f(z_1),f(z_2),\ldots,f(z_n),\ldots)$ maps generalized Nevanlinna's flat classes in a domain $G$ of a complex plane in $l^p$.

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