A class of integral operators on the unit ball of ℂn

Osman Kures; Kehe Zhu

doi:10.1007/s00020-005-1411-3

A class of integral operators on the unit ball of ℂⁿ

Osman Kures
, Kehe Zhu

Mathematics and Statistics

University at Albany

SUNY Albany

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator Tf(z) = (1 - |z| ²)^a ∫_{script B signn} (1 - |w| ²)^b/(1 - <z, w>)^c f(w)du(w) is bounded on L^p(script B sign_n, dv_t), where script B sign_n is the open unit ball in ℂⁿ, 1 ≤ p < ∞ and dv_t(z) = (1 - |z|²)^t dv (z) with dv being volume measure on script B sign_n. The characterization remains the same if we replace (1 - <z, w>)^c in the integral kernel above by its modulus |1 - <z, w>|^c.

Original language	English
Pages (from-to)	71-82
Number of pages	12
Journal	Integral Equations and Operator Theory
Volume	56
Issue number	1
DOIs	https://doi.org/10.1007/s00020-005-1411-3
State	Published - Sep 2006

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abstract = "For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator Tf(z) = (1 - |z| 2)a ∫script B signn (1 - |w| 2)b/(1 - )c f(w)du(w) is bounded on Lp(script B signn, dvt), where script B signn is the open unit ball in ℂn, 1 ≤ p < ∞ and dvt(z) = (1 - |z|2)t dv (z) with dv being volume measure on script B signn. The characterization remains the same if we replace (1 - )c in the integral kernel above by its modulus |1 - |c.",

author = "Osman Kures and Kehe Zhu",

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N2 - For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator Tf(z) = (1 - |z| 2)a ∫script B signn (1 - |w| 2)b/(1 - )c f(w)du(w) is bounded on Lp(script B signn, dvt), where script B signn is the open unit ball in ℂn, 1 ≤ p < ∞ and dvt(z) = (1 - |z|2)t dv (z) with dv being volume measure on script B signn. The characterization remains the same if we replace (1 - )c in the integral kernel above by its modulus |1 - |c.

AB - For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator Tf(z) = (1 - |z| 2)a ∫script B signn (1 - |w| 2)b/(1 - )c f(w)du(w) is bounded on Lp(script B signn, dvt), where script B signn is the open unit ball in ℂn, 1 ≤ p < ∞ and dvt(z) = (1 - |z|2)t dv (z) with dv being volume measure on script B signn. The characterization remains the same if we replace (1 - )c in the integral kernel above by its modulus |1 - |c.

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JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

ER -

A class of integral operators on the unit ball of ℂⁿ

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