L regularity of the Bergman projection on domains covered by the polydisc

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.

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Algebras Generated by the Bergman Projection and Operators of Multiplication by Piecewise Continuous Functions

Integral Equations and Operator Theory ◽

10.1007/s000200300025 ◽

2003 ◽

Vol 46 (2) ◽

pp. 215-234 ◽

Cited By ~ 8

Author(s):

Maribel Loaiza

Keyword(s):

Continuous Functions ◽

Bergman Projection ◽

Piecewise Continuous

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Projections on Bergman Spaces Over Plane Domains

Canadian Journal of Mathematics ◽

10.4153/cjm-1979-105-6 ◽

1979 ◽

Vol 31 (6) ◽

pp. 1269-1280 ◽

Cited By ~ 1

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).

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

Canadian Mathematical Bulletin ◽

10.4153/cmb-2011-186-3 ◽

2013 ◽

Vol 56 (3) ◽

pp. 593-601 ◽

Cited By ~ 3

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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On Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains inCn

Journal of Function Spaces ◽

10.1155/2014/975434 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11

Author(s):

Romi F. Shamoyan ◽

Olivera Mihić

Keyword(s):

Unit Disk ◽

Bergman Kernel ◽

Extremal Problems ◽

Bergman Projection ◽

Bounded Domains ◽

Bounded Symmetric Domains ◽

Siegel Domains ◽

Type Spaces ◽

Tube Type ◽

Homogeneous Domains

Based on recent results on boundedness of Bergman projection with positive Bergman kernel in analytic spaces in various types of domains inCn, we extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new Bergman type spaces in Lie ball, bounded symmetric domains of tube type, Siegel domains, and minimal bounded homogeneous domains.

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