Geodesic
On the Structure of Spaces of Polyanalytic Functions
Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 750-764

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Suppose that $A_mL_p(D,\alpha)$ is the space of all $m$-analytic functions on the disk $D=\{z:|z|1\}$ which are $p$th power integrable over area with the weight $(1-|z|^2)^\alpha$, $\alpha >-1$. In the paper, we introduce subspaces $A_kL_p^0(D,\alpha)$, $k=1,2,\dots,m$, of the space $A_mL_p(D,\alpha)$ and prove that $A_mL_p(D,\alpha)$ is the direct sum of these subspaces. These results are used to obtain growth estimates of derivatives of polyanalytic functions near the boundary of arbitrary domains. 
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     author = {A.-R. K. Ramazanov},
     title = {On the {Structure} of {Spaces} of {Polyanalytic} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {5},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a14/}
}
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A.-R. K. Ramazanov. On the Structure of Spaces of Polyanalytic Functions. Matematičeskie zametki, Tome 72 (2002) no. 5, pp. 750-764. http://geodesic.mathdoc.fr/item/MZM_2002_72_5_a14/