Norm of an Integral Operator Related to the Harmonic Bergman Projection

Abstract

The norm of the operatorfor a range of p and α.Mathematics Subject Classification (2010). Primary 47B38, 47G10; Secondary 32A25.

The Forelli-Rudin type theorem and a class of integral operator related to hypergeometric function

“…Zhou [17] [16,18]. 算子 S 0,λ,n+λ 在 L p 空间上的精确范数计算参见文献 [16,19]. 当 a = 2 + λ, b = λ, c = n + 2 + 2λ 时, S a,b,c 是文献 [20,21] 中讨论的调和 Berezin 型变换.…”

“…[17] 中的主要结果. 特别地, 当 T ξ,η a,b,θ 中的 a = 0, b = λ, θ = n/2, ξ = η = n + λ 时, 即 S a,b,c 中的 a = 0, b = λ, c = n + λ 时, 得到加权调和 Bergman 投 影在 L p λ (B) 上的有界性与上界估计, 这是文献 [16,19] 中的主要结果.…”

On the Forelli–Rudin Projection Theorem

“…for ℜc > 0, ℜd > 0 and ℜ(c + d − a − b) > 0. We refer to [10] for a proof. iii) Let l > 0 and let G be any function defined in an interval (0, l) with positive values.…”