Sharp Forelli–Rudin estimates and the norm of the Bergman projection

Liu, Congwen

doi:10.1016/j.jfa.2014.09.027

Cited by 36 publications

(13 citation statements)

References 8 publications

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“…Note that the conjecture agrees with the already established value for the norm of the Riesz projection due to Hollenbeck and Verbitsky [10]. However, very recently, in [13], the first author of the present paper obtained P p ≥ Γ(2/p)Γ(2/q), which disproves (1.2). However, this motivated the following conjecture.…”

Section: Introductionsupporting

confidence: 91%

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Two-sided norm estimates for Bergman-type projections with an asymptotically sharp lower bound

2018

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We obtain new two-sided norm estimates for the family of Bergmantype projections arising from the standard weights (1 − |z| 2 ) α where α > −1. As α → −1, the lower bound is sharp in the sense that it asymptotically agrees with the norm of the Riesz projection. The upper bound is estimated in terms of the maximal Bergman projection, whose exact operator norm we calculate. The results provide evidence towards a conjecture that was posed very recently by the first author.2010 Mathematics Subject Classification. Primary 32A25; Secondary 32A36, 47G10.

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Section: Introductionsupporting

confidence: 91%

“…which we conjecture to be true. When α = 0, we then recover the conjecture from [13]. The lower bound is obtained by using a suitable choice of test functions formed from Bergman-type kernels along with some interpolation, manipulation of the classical Forelli-Rudin estimates [7], and a Hausdorff-Young type inequality.…”

Section: Introductionmentioning

confidence: 82%

Two-sided norm estimates for Bergman-type projections with an asymptotically sharp lower bound

2018

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“…Since then, several nice works have been done in the direction of the sharp estimate of Bergman type operators, such as [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Sharp Weighted Bounds for Multilinear Fractional Type Operators Associated with Bergman Projection

Zhang

Senhua

Xue

2018

Journal of Function Spaces

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“…[12, Proposition 1.4.10]), we shall call the above result the Forelli-Rudin type estimates on the real ball. The purpose of this note is to present a sharp version of these estimates, which can also be viewed as an analogue of [8,Theorem 1.3] in the setting of the unit real ball. More precisely, our main results are as follows.…”

Section: Introductionmentioning

confidence: 99%