L p -estimates of extensions of holomorphic functions defined on a non-reduced subvariety
Annales de l'Institut Fourier, Volume 74 (2024) no. 2, pp. 783-809.

Let D be a strictly pseudoconvex domain in N and X a pure-dimensional non-reduced subvariety that behaves well at D. We provide L p -estimates of extensions of holomorphic functions defined on X.

Soit D un domaine strictement pseudo-convexe de N et X une sous-variété non réduite qui se comporte bien en D. Nous donnons des estimations L p des extensions de fonctions holomorphes sur X.

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DOI: 10.5802/aif.3586
Classification: 32A26, 32A27, 32A36, 32B15, 32C25, 32C30
Keywords: Interpolation, Bergman space, non-reduced subvariety.
Mot clés : Interpolation, espace de Bergman, sous-variété non réduite.
Andersson, Mats 1

1 Department of Mathematical Sciences Division of Algebra and Geometry Chalmers University of Technology and the University of Gothenburg SE-412 96 Göteborg (Sweden)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Andersson, Mats. $L^p$-estimates of extensions of holomorphic functions defined on a non-reduced subvariety. Annales de l'Institut Fourier, Volume 74 (2024) no. 2, pp. 783-809. doi : 10.5802/aif.3586. https://aif.centre-mersenne.org/articles/10.5802/aif.3586/

[1] Alexandre, William; Mazzilli, Emmanuel Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Volume 14 (2015) no. 1, pp. 293-330 | DOI | MR | Zbl

[2] Amar, Éric Extension de fonctions holomorphes et courants, Bull. Sci. Math. (2), Volume 107 (1983) no. 1, pp. 25-48 | MR | Zbl

[3] Andersson, Mats Integral representation with weights. I, Math. Ann., Volume 326 (2003) no. 1, pp. 1-18 | DOI | MR | Zbl

[4] Andersson, Mats Integral representation with weights. II. Division and interpolation, Math. Z., Volume 254 (2006) no. 2, pp. 315-332 | DOI | MR | Zbl

[5] Andersson, Mats Uniqueness and factorization of Coleff–Herrera currents, Ann. Fac. Sci. Toulouse Math. (6), Volume 18 (2009) no. 4, pp. 651-661 | DOI | Numdam | MR | Zbl

[6] Andersson, Mats Coleff–Herrera currents, duality, and Noetherian operators, Bull. Soc. Math. France, Volume 139 (2011) no. 4, pp. 535-554 | DOI | Numdam | MR | Zbl

[7] Andersson, Mats A pointwise norm on a non-reduced analytic space, J. Funct. Anal., Volume 283 (2022) no. 4, 109520, 36 pages | DOI | MR | Zbl

[8] Andersson, Mats; Lärkäng, Richard The ¯-equation on a non-reduced analytic space, Math. Ann., Volume 374 (2019) no. 1-2, pp. 553-599 | DOI | MR | Zbl

[9] Andersson, Mats; Samuelsson, Håkan A Dolbeault–Grothendieck lemma on complex spaces via Koppelman formulas, Invent. Math., Volume 190 (2012) no. 2, pp. 261-297 | DOI | MR | Zbl

[10] Andersson, Mats; Wulcan, Elizabeth Residue currents with prescribed annihilator ideals, Ann. Sci. École Norm. Sup. (4), Volume 40 (2007) no. 6, pp. 985-1007 | DOI | Numdam | MR | Zbl

[11] Andersson, Mats; Wulcan, Elizabeth Decomposition of residue currents, J. Reine Angew. Math., Volume 638 (2010), pp. 103-118 | DOI | MR | Zbl

[12] Andersson, Mats; Wulcan, Elizabeth Direct images of semi-meromorphic currents, Ann. Inst. Fourier, Volume 68 (2018) no. 2, pp. 875-900 http://aif.cedram.org/item?id=AIF_2018__68_2_875_0 | DOI | Numdam | MR | Zbl

[13] Barlet, Daniel Le faisceau ω X sur un espace analytique X de dimension pure, Fonctions de plusieurs variables complexes, III (Sém. François Norguet, 1975–1977) (Lecture Notes in Mathematics), Volume 670, Springer, Berlin, 1978, pp. 187-204 | MR | Zbl

[14] Björk, Jan-Erik Residues and 𝒟-modules, The legacy of Niels Henrik Abel, Springer, Berlin, 2004, pp. 605-651 | DOI | MR | Zbl

[15] Cao, JunYan; Demailly, Jean-Pierre; Matsumura, Shin-ichi A general extension theorem for cohomology classes on non reduced analytic subspaces, Sci. China Math., Volume 60 (2017) no. 6, pp. 949-962 | DOI | MR | Zbl

[16] Cumenge, Anne Extension dans des classes de Hardy de fonctions holomorphes et estimations de type « mesures de Carleson » pour l’équation ¯, Ann. Inst. Fourier, Volume 33 (1983) no. 3, pp. 59-97 | DOI | Numdam | MR | Zbl

[17] Demailly, Jean-Pierre Extension of holomorphic functions defined on non reduced analytic subvarieties, The legacy of Bernhard Riemann after one hundred and fifty years. Vol. I (Adv. Lect. Math. (ALM)), Volume 35, Int. Press, Somerville, MA, 2016, pp. 191-222 | MR | Zbl

[18] Henkin, Gennadi; Leiterer, Jürgen Theory of functions on complex manifolds, Monographs in Mathematics, 79, Birkhäuser Verlag, Basel, 1984, 226 pages | MR | Zbl

[19] Kerzman, N.; Stein, E. M. The Szegő kernel in terms of Cauchy–Fantappiè kernels, Duke Math. J., Volume 45 (1978) no. 2, pp. 197-224 http://projecteuclid.org/euclid.dmj/1077312816 | DOI | MR | Zbl

[20] Ohsawa, Takeo A survey on the L 2 extension theorems, J. Geom. Anal., Volume 30 (2020) no. 2, pp. 1366-1395 | DOI | MR | Zbl

[21] Ohsawa, Takeo; Takegoshi, Kenshō On the extension of L 2 holomorphic functions, Math. Z., Volume 195 (1987) no. 2, pp. 197-204 | DOI | MR | Zbl

[22] Range, R. Michael Holomorphic functions and integral representations in several complex variables, Graduate Texts in Mathematics, 108, Springer-Verlag, New York, 1986, xx+386 pages | DOI | MR | Zbl

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