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Formulas for Derivatives of Solutions of the \( \bar \partial \) -Equation in the Ball

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Topics in Analysis and its Applications

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry ((NAII,volume 147))

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Abstract

Letf ∫(z)=\( \sum\nolimits_{k = 1}^n {f_k (z)d\bar z_k } \) be a closed (0, 1) form in the unit ball B∈ℂn, and let ua be the solution of the equation \( \bar \partial \) u=∫, which has the minimal norm in the weighted space L2[(1-|z|2)adv]. Some explicit integral formulas for the derivatives of ua are obtained. These formulas are used for estimations of the derivatives of ua(z) in Cm-norm. Similar formulas and estimates are obtained also for the derivatives of the “canonical” solution having the minimal L2-norm on the unit sphere.

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References

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Author information

Authors and Affiliations

  1. Yerevan State University, Aleck Manookian str. 1, Yerevan, 375049, Armenia

    A. I. Petrosyan

Authors
  1. A. I. Petrosyan
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Editor information

Editors and Affiliations

  1. Institute of Mathematics of National Academy of Sciences of Armenia, Yerevan, Armenia

    G. A. Barsegian

  2. Mathematical Institute, Freie Universität Berlin, Berlin, Germany

    H. G. W. Begehr

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© 2004 Kluwer Academic Publishers

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Petrosyan, A.I. (2004). Formulas for Derivatives of Solutions of the \( \bar \partial \) -Equation in the Ball. In: Barsegian, G.A., Begehr, H.G.W. (eds) Topics in Analysis and its Applications. NATO Science Series II: Mathematics, Physics and Chemistry, vol 147. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2128-3_15

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