We study weighted extremal functions on a compact subset of C n when the weight is fixed andthe logarithmic growth parameter varies. Concavity and two-sided estimates show that the regular param-eters at a point form either the empty set, the smallest contact parameter alone, or the whole contact ray.At a regular parameter, we estimate the right derivative and characterize both persistence of regularity andequality of this derivative with the unweighted Green function. A local estimate involving dd c shows thata global admissible extension that is strictly plurisubharmonic near the point makes weighted regularityequivalent to local pluriregularity. We also describe failure of local pluriregularity by removing a negligiblesubset. This gives a characterization of the points at which a compact set is non-plurithin but not locallypluriregular, and identifies its largest relatively plurifine open negligible subset. The paper presents a focusedaccount of these results from the author’s longer preprint.
| Mualliflar | Narzillaev, Nurbek |
|---|---|
| Jurnal | Ўзбекистон Миллий университети хабарлари |
| Nashriyot | Ўзбекистон Миллий университети |
| ISSN | 2181-7324, 3093-8996 |
| Nashr sanasi | 2026-10-07 |
| Jild | 2 |
| Son | 2.3 |
| Betlar | 146-152 |
| Til | Ingliz |
| Indeksga qo‘shilgan | 2026-10-08 |
weighted extremal function, local pluriregularity, plurithinness, negligible set, plurifine topol- ogy.
| APA | Narzillaev, Nurbek (2026). Regular parameters and local pluriregularity. Ўзбекистон Миллий университети хабарлари, 2(2.3), 146-152. https://journals.nuu.uz/index.php/actanuuz/article/view/15262 |
|---|---|
| GOST (OAK) | Narzillaev, Nurbek Regular parameters and local pluriregularity // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 146-152. |
| MLA | Narzillaev, Nurbek. “Regular parameters and local pluriregularity.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 146-152, 2026. https://journals.nuu.uz/index.php/actanuuz/article/view/15262 |
| Chicago | Narzillaev, Nurbek. “Regular parameters and local pluriregularity.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 146-152 (2026). https://journals.nuu.uz/index.php/actanuuz/article/view/15262 |
| Harvard | Narzillaev, Nurbek (2026) ‘Regular parameters and local pluriregularity’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 146-152. https://journals.nuu.uz/index.php/actanuuz/article/view/15262 |
| BibTeX | @article{narzillaevnurbek2026,
title = {Regular parameters and local pluriregularity},
author = {Narzillaev, Nurbek},
journal = {Ўзбекистон Миллий университети хабарлари},
year = {2026},
volume = {2},
number = {2.3},
pages = {146-152},
url = {https://journals.nuu.uz/index.php/actanuuz/article/view/15262}
} |
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