scholarly journals Mapping properties of weighted Bergman projection operators on Reinhardt domains

2016 ◽  
Vol 144 (8) ◽  
pp. 3479-3491 ◽  
Author(s):  
Željko Čučković ◽  
Yunus E. Zeytuncu
Keyword(s):  
Bergman Projection ◽  
Projection Operators ◽  
Reinhardt Domains ◽  
Weighted Bergman Projection

Mapping properties of the Bergman projections on elementary Reinhardt domains

2021 ◽  
Vol 71 (4) ◽  
pp. 831-844
Author(s):  
Shuo Zhang
Keyword(s):  
Sobolev Spaces ◽  
Bergman Projection ◽  
Reinhardt Domain ◽  
Reinhardt Domains ◽  
Multi Index ◽  
Bergman Projections

Abstract The elementary Reinhardt domain associated to multi-index k = (k 1, …, k n ) ∈ ℤ n is defined by ℋ ( k ) : = { z ∈ D n : z k   is defined and   | z k | < 1 } . $$\mathcal{H}(\mathbf{k}):=\{z\in\mathbb{D}^n: z^{\mathbf{k}}\ \text{is defined and}\ |z^{\mathbf{k}}|<1\}.$$ In this paper, we study the mapping properties of the associated Bergman projection on L p spaces and L p Sobolev spaces of order ≥ 1.

On the p-norm of an Integral Operator in the Half Plane

2013 ◽  
Vol 56 (3) ◽  
pp. 593-601 ◽  
Author(s):  
Congwen Liu ◽  
Lifang Zhou
Keyword(s):  
Integral Operator ◽  
Half Plane ◽  
Integral Operators ◽  
Bergman Projection ◽  
Partial Answer ◽  
Upper Half Plane ◽  
Weighted Bergman Projection

Abstract.We give a partial answer to a conjecture of Dostanić on the determination of the norm of a class of integral operators induced by the weighted Bergman projection in the upper half plane.

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.

scholarly journals Norm of the Bergman Projection

2014 ◽  
Vol 115 (1) ◽  
pp. 143 ◽  
Author(s):  
David Kalaj ◽  
Marijan Marković
Keyword(s):  
Unit Ball ◽  
Projection Operator ◽  
Bloch Space ◽  
Bergman Projection ◽  
Invariant Norm ◽  
Weighted Bergman Projection ◽  
Special Case

This paper deals with the the norm of the weighted Bergman projection operator $P_{\alpha}:L^\infty(B)\rightarrow\mathscr{B}$ where $\alpha > - 1$ and $\mathscr{B}$ is the Bloch space of the unit ball $B$ of the $\mathsf{C}^n$. We consider two Bloch norms, the standard Bloch norm and invariant norm w.r.t. automorphisms of the unit ball. Our work contains as a special case the main result of the recent paper [6].

scholarly journals A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-7
Author(s):  
Yufeng Lu ◽  
Jun Yang
Keyword(s):  
Linear Operator ◽  
Unit Ball ◽  
Bounded Linear Operator ◽  
Hankel Operator ◽  
Bergman Spaces ◽  
Bergman Projection ◽  
Weighted Bergman Spaces ◽  
Bounded Linear ◽  
Weighted Bergman Projection

This paper shows that ifSis a bounded linear operator acting on the weighted Bergman spacesAα2on the unit ball inℂnsuch thatSTzi=Tz¯iS (i=1,…,n), whereTzi=zifandTz¯i=P(z¯if); and wherePis the weighted Bergman projection, thenSmust be a Hankel operator.

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