scholarly journals Lp-REGULARITY OF THE BERGMAN PROJECTION ON QUOTIENT DOMAINS

2021 ◽  
pp. 1-37
Author(s):  
CHASE BENDER ◽  
DEBRAJ CHAKRABARTI ◽  
LUKE EDHOLM ◽  
MEERA MAINKAR
Keyword(s):  
Bergman Projection ◽  
Lp Regularity

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

scholarly journals Norm estimation of the harmonic Bergman projection on half-spaces

2009 ◽  
Vol 61 (1) ◽  
pp. 225-235 ◽  
Author(s):  
Hyungwoon KOO ◽  
Kyesook NAM ◽  
HeungSu YI
Keyword(s):  
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.

Projections on Bergman Spaces Over Plane Domains

1979 ◽  
Vol 31 (6) ◽  
pp. 1269-1280 ◽  
Author(s):  
Jacob Burbea
Keyword(s):  
Bergman Kernel ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Plane Domain ◽  
Bergman Projection ◽  
Lebesgue Spaces ◽  
Lebesque Measure ◽  
Image Position

Let D be a bounded plane domain and let Lp(D) stand for the usual Lebesgue spaces of functions with domain D, relative to the area Lebesque measure dσ(z) = dxdy. The class of all holomorphic functions in D will be denoted by H(D) and we write Bp(D) = Lp(D) ∩ H(D). Bp(D) is called the Bergman p-space and its norm is given byLet be the Bergman kernel of D and consider the Bergman projection(1.1)It is well known that P is not bounded on Lp(D), p = 1, ∞, and moreover, it can be shown that there are no bounded projections of L∞(Δ) onto B∞(Δ).

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.

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