Two-sided norm estimate for the Bergman projection on the Besov space in the unit ball in $\mathbb{C}^{n}$

2018 ◽  
Vol 93 (3-4) ◽  
pp. 263-284
Author(s):  
Djordjije Vujadinovic
Keyword(s):  
Unit Ball ◽  
Besov Space ◽  
Bergman Projection ◽  
Norm Estimate

scholarly journals A Sharp Constant for the Bergman Projection

2015 ◽  
Vol 58 (1) ◽  
pp. 128-133 ◽  
Author(s):  
Marijan Marković
Keyword(s):  
Unit Ball ◽  
Besov Space ◽  
Projection Operator ◽  
Bergman Projection ◽  
Hyperbolic Metric ◽  
Sharp Constant ◽  
The Hyperbolic Metric

AbstractFor the Bergman projection operator P we prove thatHere λ stands for the hyperbolic metric in the unit ball B of Cn, and B1 denotes the Besov space with an adequate semi-norm. We also consider a generalization of this result. This generalizes some recent results due to Perälä.

scholarly journals Weighted estimates for the Berezin transform and Bergman projection on the unit ball

2016 ◽  
Vol 286 (3-4) ◽  
pp. 1465-1478 ◽  
Author(s):  
Rob Rahm ◽  
Edgar Tchoundja ◽  
Brett D. Wick
Keyword(s):  
Unit Ball ◽  
Berezin Transform ◽  
Bergman Projection ◽  
Weighted Estimates

scholarly journals Extended Cesáro operators between generalized Besov spaces and Bloch type spaces in the unit ball

2009 ◽  
Vol 7 (3) ◽  
pp. 209-223 ◽  
Author(s):  
Ze-Hua Zhou ◽  
Min Zhu
Keyword(s):  
Unit Ball ◽  
Besov Space ◽  
Besov Spaces ◽  
Complex Space ◽  
Bloch Space ◽  
Sufficient Conditions ◽  
Cesàro Operator ◽  
Type Spaces ◽  
Necessary And Sufficient ◽  
Cesaro Operator

Let 𝑔 be a holomorphic of the unit ballBin then-dimensional complex space, and denote byTgthe extended Cesáro operator with symbolg. Let 0 <p< +∞, −n− 1 <q< +∞,q> −1 and α > 0, starting with a brief introduction to well known results about Cesáro operator, we investigate the boundedness and compactness ofTgbetween generalized Besov spaceB(p, q)and 𝛼α- Bloch spaceℬαin the unit ball, and also present some necessary and sufficient conditions.

scholarly journals Optimal norm estimate of operators related to the harmonic Bergman projection on the ball

2010 ◽  
Vol 62 (3) ◽  
pp. 357-374 ◽  
Author(s):  
Boo Rim Choe ◽  
Hyungwoon Koo ◽  
Kyesook Nam
Keyword(s):  
Bergman Projection ◽  
Norm Estimate ◽  
Optimal Norm

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].

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