scholarly journals WEIGHTED INTEGRAL REPRESENTATIONS IN TUBE DOMAIN OVER REAL UNIT BALL

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
ARMAN H. KARAPETYAN
Keyword(s):  
Unit Ball ◽  
Integral Representations ◽  
Tube Domain ◽  
Weighted Integral

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 ).

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 On the global operator and Fueter mapping theorem for slice polyanalytic functions

2020 ◽  
pp. 1-24
Author(s):  
Daniel Alpay ◽  
Kamal Diki ◽  
Irene Sabadini
Keyword(s):  
Unit Ball ◽  
Integral Representations ◽  
Axially Symmetric ◽  
Regular Functions ◽  
Slice Hyperholomorphic Functions ◽  
Hyperholomorphic Functions ◽  
Global Operator ◽  
Polyanalytic Functions

In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions. We investigate also an extension version of the Fueter mapping theorem in this polyanalytic setting. In particular, we show that under axially symmetric conditions it is always possible to construct Fueter regular and poly-Fueter regular functions through slice polyanalytic ones using what we call the poly-Fueter mappings. We study also some integral representations of these results on the quaternionic unit ball.

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 $|w|^{2\varphi}\cdot(1-|w|^{2\rho})^{\beta}$.

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