Poly-Bergman Projections and Orthogonal Decompositions of L 2-spaces Over Bounded Domains

2008 ◽  
pp. 263-282 ◽  
Author(s):  
Yuri I. Karlovich ◽  
Luís V. Pessoa
Keyword(s):  
Bounded Domains ◽  
Orthogonal Decompositions ◽  
Bergman Projections

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.

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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