scholarly journals Pointwise estimates for the weighted Bergman projection kernel in ${\Bbb C}^n$, using a weighted $L^2$ estimate for the $\bar\partial$ equation

1998 ◽  
Vol 48 (4) ◽  
pp. 967-997 ◽  
Author(s):  
Henrik Delin
Keyword(s):  
Bergman Projection ◽  
Pointwise Estimates ◽  
Weighted Bergman Projection

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 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.

REGULARITY OF THE WEIGHTED BERGMAN PROJECTION ON THE FOCK–BARGMANN–HARTOGS DOMAIN

2020 ◽  
Vol 102 (2) ◽  
pp. 282-292
Author(s):  
LE HE ◽  
YANYAN TANG ◽  
ZHENHAN TU
Keyword(s):  
Bergman Kernel ◽  
Pseudoconvex Domain ◽  
Regularity Result ◽  
Bergman Projection ◽  
Trivial Case ◽  
Hartogs Domain ◽  
Strongly Pseudoconvex Domain ◽  
Real Analytic ◽  
Weighted Bergman Projection ◽  
Weighted Bergman Kernel

The Fock–Bargmann–Hartogs domain $D_{n,m}(\,\unicode[STIX]{x1D707}):=\{(z,w)\in \mathbb{C}^{n}\times \mathbb{C}^{m}:\Vert w\Vert ^{2}<e^{-\unicode[STIX]{x1D707}\Vert z\Vert ^{2}}\}$, where $\unicode[STIX]{x1D707}>0$, is an unbounded strongly pseudoconvex domain with smooth real-analytic boundary. We compute the weighted Bergman kernel of $D_{n,m}(\,\unicode[STIX]{x1D707})$ with respect to the weight $(-\unicode[STIX]{x1D70C})^{\unicode[STIX]{x1D6FC}}$, where $\unicode[STIX]{x1D70C}(z,w):=\Vert w\Vert ^{2}-e^{-\unicode[STIX]{x1D707}\Vert z\Vert ^{2}}$ and $\unicode[STIX]{x1D6FC}>-1$. Then, for $p\in [1,\infty ),$ we show that the corresponding weighted Bergman projection $P_{D_{n,m}(\,\unicode[STIX]{x1D707}),(-\unicode[STIX]{x1D70C})^{\unicode[STIX]{x1D6FC}}}$ is unbounded on $L^{p}(D_{n,m}(\,\unicode[STIX]{x1D707}),(-\unicode[STIX]{x1D70C})^{\unicode[STIX]{x1D6FC}})$, except for the trivial case $p=2$. This gives an example of an unbounded strongly pseudoconvex domain whose ordinary Bergman projection is $L^{p}$ irregular when $p\in [1,\infty )\setminus \{2\}$, in contrast to the well-known positive $L^{p}$ regularity result on a bounded strongly pseudoconvex domain.

scholarly journals Pointwise estimates for higher order convexity preserving polynomial approximation

1994 ◽  
Vol 36 (2) ◽  
pp. 213-233 ◽  
Author(s):  
Jia-Ding Cao ◽  
Heinz H. Gonska
Keyword(s):  
Polynomial Approximation ◽  
Convex Functions ◽  
Higher Order ◽  
Second Order ◽  
Convolution Type ◽  
Shape Preservation ◽  
Moduli Of Continuity ◽  
Pointwise Estimates ◽  
Higher Order Convexity ◽  
Boolean Sum

AbstractDeVore-Gopengauz-type operators have attracted some interest over the recent years. Here we investigate their relationship to shape preservation. We construct certain positive convolution-type operators Hn, s, j which leave the cones of j-convex functions invariant and give Timan-type inequalities for these. We also consider Boolean sum modifications of the operators Hn, s, j show that they basically have the same shape preservation behavior while interpolating at the endpoints of [−1, 1], and also satisfy Telyakovskiῐ- and DeVore-Gopengauz-type inequalities involving the first and second order moduli of continuity, respectively. Our results thus generalize related results by Lorentz and Zeller, Shvedov, Beatson, DeVore, Yu and Leviatan.

scholarly journals Bergman projection induced by radial weight

2021 ◽  
Vol 391 ◽  
pp. 107950
Author(s):  
José Ángel Peláez ◽  
Jouni Rättyä
Keyword(s):  
Bergman Projection ◽  
Radial Weight
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