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On a theorem of Cartwright in higher dimensions. / Logunov, A.; Malinnikova, E.; Mozolyako, P.

In: Journal of the London Mathematical Society, No. 1, 2015, p. 65-82.

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Harvard

Logunov, A, Malinnikova, E & Mozolyako, P 2015, 'On a theorem of Cartwright in higher dimensions', Journal of the London Mathematical Society, no. 1, pp. 65-82. https://doi.org/10.1112/jlms/jdv060

APA

Logunov, A., Malinnikova, E., & Mozolyako, P. (2015). On a theorem of Cartwright in higher dimensions. Journal of the London Mathematical Society, (1), 65-82. https://doi.org/10.1112/jlms/jdv060

Vancouver

Logunov A, Malinnikova E, Mozolyako P. On a theorem of Cartwright in higher dimensions. Journal of the London Mathematical Society. 2015;(1):65-82. https://doi.org/10.1112/jlms/jdv060

Author

Logunov, A. ; Malinnikova, E. ; Mozolyako, P. / On a theorem of Cartwright in higher dimensions. In: Journal of the London Mathematical Society. 2015 ; No. 1. pp. 65-82.

BibTeX

@article{a4fba0683c6241cf813814794d60cf99,
title = "On a theorem of Cartwright in higher dimensions",
abstract = "{\textcopyright} 2015 London Mathematical Society.We consider harmonic functions in the unit ball of Rn+1 that are unbounded near the boundary, but can be estimated from above by some (rapidly increasing) radial weight w. Our main result gives some conditions on w that guarantee the estimate from below on the harmonic function by a multiple of this weight. In dimension 2, this reverse estimate was first obtained by Cartwright for the case of the power weights, wp(z) = (1 - |z|)-p, p>1, and then generalized to a wide class of regular weights by a number of authors.",
author = "A. Logunov and E. Malinnikova and P. Mozolyako",
year = "2015",
doi = "10.1112/jlms/jdv060",
language = "English",
pages = "65--82",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "1",

}

RIS

TY - JOUR

T1 - On a theorem of Cartwright in higher dimensions

AU - Logunov, A.

AU - Malinnikova, E.

AU - Mozolyako, P.

PY - 2015

Y1 - 2015

N2 - © 2015 London Mathematical Society.We consider harmonic functions in the unit ball of Rn+1 that are unbounded near the boundary, but can be estimated from above by some (rapidly increasing) radial weight w. Our main result gives some conditions on w that guarantee the estimate from below on the harmonic function by a multiple of this weight. In dimension 2, this reverse estimate was first obtained by Cartwright for the case of the power weights, wp(z) = (1 - |z|)-p, p>1, and then generalized to a wide class of regular weights by a number of authors.

AB - © 2015 London Mathematical Society.We consider harmonic functions in the unit ball of Rn+1 that are unbounded near the boundary, but can be estimated from above by some (rapidly increasing) radial weight w. Our main result gives some conditions on w that guarantee the estimate from below on the harmonic function by a multiple of this weight. In dimension 2, this reverse estimate was first obtained by Cartwright for the case of the power weights, wp(z) = (1 - |z|)-p, p>1, and then generalized to a wide class of regular weights by a number of authors.

U2 - 10.1112/jlms/jdv060

DO - 10.1112/jlms/jdv060

M3 - Article

SP - 65

EP - 82

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 1

ER -

ID: 3990955