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Mat. Zametki, 2002, Volume 72, Issue 5, Pages 750–764 (Mi mz465)  

This article is cited in 8 scientific papers (total in 8 papers)

On the Structure of Spaces of Polyanalytic Functions

A.-R. K. Ramazanov

Kaluga Branch of Bauman Moscow State Technical University

Abstract: Suppose that $A_mL_p(D,\alpha)$ is the space of all $m$-analytic functions on the disk $D=ż:|z|<1\}$ which are $p$th power integrable over area with the weight $(1-|z|^2)^\alpha$, $\alpha >-1$. In the paper, we introduce subspaces $A_kL_p^0(D,\alpha)$, $k=1,2,…,m$, 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.

DOI: https://doi.org/10.4213/mzm465

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English version:
Mathematical Notes, 2002, 72:5, 692–704

Bibliographic databases:

UDC: 517.5
Received: 13.02.2001
Revised: 16.10.2001

Citation: A.-R. K. Ramazanov, “On the Structure of Spaces of Polyanalytic Functions”, Mat. Zametki, 72:5 (2002), 750–764; Math. Notes, 72:5 (2002), 692–704

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. K. Ramazanov, “Estimate of the Norm of a Polyanalytic Function via the Norm of Its Polyharmonic Component”, Math. Notes, 75:4 (2004), 568–573  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Du, JY, “Mixed boundary value problem for some pairs of metaanalytic function and analytic function”, Mathematical Methods in the Applied Sciences, 31:15 (2008), 1761  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Wang Y., Du J.Yu., “Haseman Boundary Value Problems for Metaanalytic Functions with Different Shifts on the Unit Circumference”, Complex Var. Elliptic Equ., 53:4 (2008), 325–342  crossref  mathscinet  zmath  isi
    4. Wang Y., Du J., “On Haseman boundary value problem for a class of metaanalytic functions with different factors on the unit circumference”, Mathematical Methods in the Applied Sciences, 33:5 (2010), 576–584  mathscinet  zmath  isi
    5. Cuckovic Z., Le T., “Toeplitz Operators on Bergman Spaces of Polyanalytic Functions”, Bull. London Math. Soc., 44:Part 5 (2012), 961–973  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Abreu L.D., Groechenig K., “Banach Gabor Frames with Hermite Functions: Polyanalytic Spaces From the Heisenberg Group”, Appl. Anal., 91:11 (2012), 1981–1997  crossref  mathscinet  zmath  isi  scopus  scopus
    7. V. I. Danchenko, “Cauchy and Poisson formulas for polyanalytic functions and applications”, Russian Math. (Iz. VUZ), 60:1 (2016), 11–21  mathnet  crossref  isi
    8. Daghighi A., “A Necessary Condition For Weak Maximum Modulus Sets of 2-Analytic Functions”, Collect. Math., 69:2 (2018), 173–180  crossref  mathscinet  zmath  isi  scopus  scopus
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