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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 265092, 27 pages
Research Article

Weighted πœ• -Integral Representations of 𝐢 𝟏 -Functions in 𝐢 𝑛

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

Received 28 July 2011; Accepted 13 August 2011

Academic Editor: Richard Rochberg

Copyright © 2012 Arman H. Karapetyan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For 𝐢 1 -functions 𝑓 , given in the complex space 𝐢 𝑛 , integral representations of the form 𝑓 = 𝑃 ( 𝑓 ) βˆ’ 𝑇 ( πœ• 𝑓 ) are obtained. Here, 𝑃 is the orthogonal projector of the space 𝐿 2 { 𝐢 𝑛 ; 𝑒 βˆ’ 𝜎 | 𝑧 | 𝜌 | 𝑧 | 𝛾 𝑑 π‘š ( 𝑧 ) } onto its subspace of entire functions and the integral operator 𝑇 appears by means of explicitly constructed kernel Φ which is investigated in detail.