Right inverse operators for the Bergman projection and biholomorphic mappings on Gevrey bounded domains

1984 ◽  
Vol 43 (1) ◽  
pp. 57-65
Author(s):  
Bernd Droste
Keyword(s):  
Bergman Projection ◽  
Bounded Domains

scholarly journals On Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains inCn

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Romi F. Shamoyan ◽  
Olivera Mihić
Keyword(s):  
Unit Disk ◽  
Bergman Kernel ◽  
Extremal Problems ◽  
Bergman Projection ◽  
Bounded Domains ◽  
Bounded Symmetric Domains ◽  
Siegel Domains ◽  
Type Spaces ◽  
Tube Type ◽  
Homogeneous Domains

Based on recent results on boundedness of Bergman projection with positive Bergman kernel in analytic spaces in various types of domains inCn, we extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new Bergman type spaces in Lie ball, bounded symmetric domains of tube type, Siegel domains, and minimal bounded homogeneous domains.

scholarly journals L∞-Estimates of the Bergman projection in the Lie ball ofℂn

2011 ◽  
Vol 9 (2) ◽  
pp. 109-128 ◽  
Author(s):  
Cyrille Nana
Keyword(s):  
Bergman Projection ◽  
The Other ◽  
Bounded Domains ◽  
Cayley Transform ◽  
Bounded Symmetric Domains ◽  
Bergman Projections

In this paper, we consider estimates with loss for the Bergman projections of bounded symmetric domains ofℂnin their Harish-Chandra realizations. This paper is twofold: on one side we develop transfer methods between these bounded domains and their Cayley transform; on the other side we give a new range ofqsuch that the Bergman projection is bounded fromL∞(ℬn)toLq(ℬn)whereℬnis the Lie ball ofℂn.

scholarly journals A note on smoothing properties of the Bergman projection

2016 ◽  
Vol 27 (11) ◽  
pp. 1650087 ◽  
Author(s):  
Sivaguru Ravisankar ◽  
Yunus E. Zeytuncu
Keyword(s):  
Holomorphic Functions ◽  
Bergman Projection ◽  
Bounded Domains ◽  
Satisfy Condition ◽  
Reinhardt Domains ◽  
Smoothing Property

Recently Herbig, McNeal, and Straube have showed that the Bergman projection of conjugate holomorphic functions is smooth up to the boundary on smoothly bounded domains that satisfy condition R. We show that a further smoothing property holds on a family of Reinhardt domains; namely, the Bergman projection of conjugate holomorphic functions is holomorphic past the boundary.

Fractional abstract Cauchy problem on complex interpolation scales

2020 ◽  
Vol 23 (4) ◽  
pp. 1125-1140
Author(s):  
Andriy Lopushansky ◽  
Oleh Lopushansky ◽  
Anna Szpila
Keyword(s):  
Cauchy Problem ◽  
Time Derivative ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Sectorial Operator ◽  
Complex Interpolation ◽  
Bounded Domains ◽  
Initial Boundary Value Problems ◽  
Fractional Time Derivative ◽  
Initial Boundary Value

AbstractAn fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.

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