×

On the extension of \(L^2\) holomorphic functions. V: Effects of generalization. (English) Zbl 0986.32002

Nagoya Math. J. 161, 1-21 (2001); erratum ibid. 163, 229 (2001).
From the abstract: “A general extension theorem for \(L^2\) holomorphic bundle-valued top forms is formulated. Although its proof is based on a principle similar to Ohsawa-Takegoshi’s extension theorem, it explains previous \(L^2\) extendability results systematically and bridges extension theory and division theory.”
In fact, the general extension theorem presented here contains all earlier results in this direction. Moreover, additional applications are given: an extended version of Skoda’s \(L^2\)-division theorem, a multidimensional form of Suita’s conjecture and a new proof of the equality between the upper uniform density of a certain set in the plane (or in the unit disc) and its so-called canonical capacity.
For parts I–IV see T. Ohsawa and K. Takegoshi, Math. Z. 195, 197-204 (1987; Zbl 0625.32011), T. Ohsawa, Publ. Res. Inst. Math. Sci. 24, No. 2, 265-275 (1988; Zbl 0653.32012), Math. Z. 219, No. 2, 215-225 (1995; Zbl 0823.32006) and Geometry and analysis on complex manifolds. Festschrift for Professor S. Kobayashi’s 60th birthday. Singapore: World Scientific. 157-170 (1994; Zbl 0884.32012).

MSC:

32A36 Bergman spaces of functions in several complex variables
Full Text: DOI

References:

[1] DOI: 10.1007/BF01244300 · Zbl 0789.30025 · doi:10.1007/BF01244300
[2] J. Reine Angew. Math 429 pp 107– (1992)
[3] DOI: 10.1007/BF01166457 · Zbl 0625.32011 · doi:10.1007/BF01166457
[4] Geometry and Analysis on Complex Manifolds, Festschrift for Prof. S. Kobayashi, World Sci pp 157– (1994)
[5] Nagoya Math. J 137 pp 145– (1995) · Zbl 0817.32013 · doi:10.1017/S0027763000005092
[6] DOI: 10.1007/BF02571643 · Zbl 0789.32015 · doi:10.1007/BF02571643
[7] DOI: 10.1007/BF02572360 · Zbl 0823.32006 · doi:10.1007/BF02572360
[8] DOI: 10.1007/s002080050177 · Zbl 0955.32019 · doi:10.1007/s002080050177
[9] Nagoya Math. J 129 pp 43– (1993) · Zbl 0774.32016 · doi:10.1017/S0027763000004311
[10] DOI: 10.1016/0001-8708(82)90028-7 · Zbl 0504.32016 · doi:10.1016/0001-8708(82)90028-7
[11] Complex Analysis and Geometry pp 285– (1993)
[12] DOI: 10.1007/BF01354665 · Zbl 0073.30203 · doi:10.1007/BF01354665
[13] DOI: 10.2977/prims/1195175200 · Zbl 0653.32012 · doi:10.2977/prims/1195175200
[14] Math. Ann 273 pp 371– (1986)
[15] Publ.. RIMS, Kyoto Univ 15 pp 929– (1980)
[16] Math. Ann 264 pp 475– (1984)
[17] Séminaire Pierre Lelong-Henri Skoda (Analysis), 1980/1981, and Colloquium at Wimereux pp 77– (1981)
[18] J. Reine. Angew. Math 464 pp 109– (1995)
[19] DOI: 10.1007/BF01453566 · Zbl 0698.47020 · doi:10.1007/BF01453566
[20] DOI: 10.1007/s002080050198 · Zbl 0912.32021 · doi:10.1007/s002080050198
[21] Arch. Rational Mech. Anal 46 pp 212– (1972)
[22] Séminaire Pierre Lelong-Henri Skoda (Analyse), Années 1978/79 LNM 822 pp 259– (1980)
[23] Ann. Sci. Ecole Norm. Sup 11 pp 577– (1978) · Zbl 0403.32019 · doi:10.24033/asens.1357
[24] Ann. Sci. Ec. Norm. Sup 5 pp 545– (1972) · Zbl 0254.32017 · doi:10.24033/asens.1237
[25] DOI: 10.1007/BF01390170 · Zbl 0343.32014 · doi:10.1007/BF01390170
[26] J. Reine Angew. Math 429 pp 91– (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.