Holomorphic functions which are highly nonintegrable at the boundary
Globevnik, Josip, 1945-
V članku pokažemo, da na omejenem kompleksnem območju ▫$D$▫ obstaja holomorfna funkcija, ki je na robu območja popolnoma neintegrabilna. Velja izrek: Naj bo ▫$D \subset \mathbb C^N$▫ omejeno ...kompleksno območje z robom razreda ▫${\cal C}^1$▫ in naj bo ▫$\varphi$▫ pozitivna zvezna funkcija na ▫$D$▫. Potem obstaja holomorfna funkcija ▫$f$▫ na ▫$D$▫ z naslednjo lastnostjo: naj bo ▫$z \in bD$▫, naj bo ▫$U \in \mathbb C^N$▫ odprta okolica točke ▫$z$▫, naj bo ▫$M$▫ realna podmnogoterost v ▫$U$▫ razreda ▫${\cal C}^1$▫, ki seče ▫$bD$▫ v ▫$z$▫ transverzalno, in naj bo ▫$dS$▫ ploščinska mera na ▫$M$▫. Potem velja ▫$$\int_{M \cap D}|f|\varphi dS = +\infty.$$▫
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