Weighted Integral Representations of Pluriharmonic Functions in the Siegel Domain of $$C^n$$

2019 ◽  
Vol 74 (4) ◽  
Author(s):  
A. H. Karapetyan
Keyword(s):  
Integral Representations ◽  
Siegel Domain ◽  
Weighted Integral ◽  
Pluriharmonic Functions

Integral Representations and Continuous Projectors in Some Spaces of Analytic and Pluriharmonic Functions

2008 ◽  
Vol 15 (4) ◽  
pp. 739-752
Author(s):  
Gigla Oniani ◽  
Lamara Tsibadze
Keyword(s):  
Integral Representations ◽  
Fractional Integrals ◽  
Boundary Values ◽  
Pluriharmonic Functions

Abstract We consider analytic and pluriharmonic functions belonging to the classes 𝐵𝑝(Ω) and 𝑏𝑝(Ω) and defined in the ball . The theorems established in the paper make it possible to obtain some integral representations of functions of the above-mentioned classes. The existence of bounded projectors from the space 𝐿(ρ, Ω) into the space 𝐵𝑝(Ω) and from the space 𝐿(ρ, Ω) into the space 𝑏𝑝(Ω) is proved. Also, consideration is given to the existence of boundary values of fractional integrals of functions of the spaces 𝐵𝑝(Ω) and 𝑏𝑝(Ω).

scholarly journals Weighted -Integral Representations of -Functions in

2012 ◽  
Vol 2012 ◽  
pp. 1-27
Author(s):  
Arman H. Karapetyan
Keyword(s):  
Integral Operator ◽  
Complex Space ◽  
Entire Functions ◽  
Integral Representations ◽  
Orthogonal Projector ◽  
Weighted Integral

For -functions , given in the complex space , integral representations of the form are obtained. Here, is the orthogonal projector of the space onto its subspace of entire functions and the integral operator appears by means of explicitly constructed kernel Φ which is investigated in detail.

scholarly journals Weighted integral representations of harmonic functions in the unit disc by means of Mittag-Leffler type kernels

2021 ◽  
pp. 1-11
Author(s):  
Feliks Hayrapetyan
Keyword(s):  
Weight Function ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Integral Representations ◽  
Weighted Integral

For weighted $L^p$-classes of functions harmonic in the unit disc, we obtain a family of weighted integral representations with weight function of the type $|w|^{2\varphi}\cdot(1-|w|^{2\rho})^{\beta}$.

scholarly journals Weighted Anisotropic Integral Representations of Holomorphic Functions in the Unit Ball of

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Arman Karapetyan
Keyword(s):  
Weight Function ◽  
Unit Ball ◽  
Explicit Form ◽  
Holomorphic Functions ◽  
Integral Form ◽  
Integral Representations ◽  
Weighted Integral ◽  
Anisotropic Weight

We obtain weighted integral representations for spaces of functions holomorphic in the unit ball and belonging to area-integrable weighted -classes with “anisotropic” weight function of the type , . The corresponding kernels of these representations are estimated, written in an integral form, and even written out in an explicit form (for ).

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