TY - JOUR
T1 - Bergman norm estimates of Poisson integrals
AU - Choe, Boo Rim
AU - Koo, Hyungwoon
AU - Yi, Heungsu
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2001/3
Y1 - 2001/3
N2 - On the half space Rn × R+ , it has been known that harmonic Bergman space bp can contain a positive function only if p > 1 + 1/n. Thus, for 1 ≤ p ≤ 1 + 1/n, Poisson integrals can be bp-functions only by means of their boundary cancellation properties. In this paper, we describe what those cancellation properties explicitly are. Also, given such cancellation properties, we obtain weighted norm inequalities for Poisson integrals. As a consequence, under weighted integrability condition given by our weighted norm inequalities, we show that our cancellation properties are equivalent to the bp-containment of Poisson integrals for p under consideration. Our results are sharp in the sense that orders of our weights cannot be improved.
AB - On the half space Rn × R+ , it has been known that harmonic Bergman space bp can contain a positive function only if p > 1 + 1/n. Thus, for 1 ≤ p ≤ 1 + 1/n, Poisson integrals can be bp-functions only by means of their boundary cancellation properties. In this paper, we describe what those cancellation properties explicitly are. Also, given such cancellation properties, we obtain weighted norm inequalities for Poisson integrals. As a consequence, under weighted integrability condition given by our weighted norm inequalities, we show that our cancellation properties are equivalent to the bp-containment of Poisson integrals for p under consideration. Our results are sharp in the sense that orders of our weights cannot be improved.
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U2 - 10.1017/s0027763000022145
DO - 10.1017/s0027763000022145
M3 - Article
AN - SCOPUS:0035294732
VL - 161
SP - 85
EP - 125
JO - Nagoya Mathematical Journal
JF - Nagoya Mathematical Journal
SN - 0027-7630
ER -