Geometric Properties of a General Kohn–Nirenberg Domain in ℂ<i><sup>n</sup></i>
The Kohn–Nirenberg domains are unbounded domains in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup></semantics></math></inline-formula>. In this...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/7/1200 |
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| Summary: | The Kohn–Nirenberg domains are unbounded domains in <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup></semantics></math></inline-formula>. In this article, we modify the Kohn–Nirenberg domain <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="normal">Ω</mi><mrow><mi>K</mi><mo>,</mo><mi>L</mi></mrow></msub><mo>=</mo><mfenced separators="" open="{" close=""><mo stretchy="false">(</mo><msub><mi>z</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>z</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mfenced><mo>∈</mo><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup><mo>:</mo><mi>R</mi><mi>e</mi><msub><mi>z</mi><mi>n</mi></msub><mo>+</mo><mi>g</mi><mo>∣</mo><msub><mi>z</mi><mi>n</mi></msub><msup><mo>∣</mo><mn>2</mn></msup><mo>+</mo><msubsup><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msubsup><mrow><mo stretchy="false">(</mo><mo>∣</mo><msub><mi>z</mi><mi>j</mi></msub><msup><mo>∣</mo><mi>p</mi></msup><mo>+</mo><msub><mi>K</mi><mi>j</mi></msub><mo>∣</mo><msub><mi>z</mi><mi>j</mi></msub><msup><mo>∣</mo><mrow><mi>p</mi><mo>−</mo><mi>q</mi></mrow></msup><mi>R</mi><mi>e</mi><msubsup><mi>z</mi><mrow><mi>j</mi></mrow><mi>q</mi></msubsup><mo>+</mo><msub><mi>L</mi><mi>j</mi></msub><mo>∣</mo><msub><mi>z</mi><mi>j</mi></msub><msup><mo>∣</mo><mrow><mi>p</mi><mo>−</mo><mn>2</mn><mi>q</mi></mrow></msup><mi>I</mi><mi>m</mi><msubsup><mi>z</mi><mrow><mi>j</mi></mrow><mrow><mn>2</mn><mi>q</mi></mrow></msubsup><mo stretchy="false">)</mo></mrow><mrow><mo><</mo><mn>0</mn><mo>}</mo></mrow></mrow></semantics></math></inline-formula> and discuss the existence of supporting surface and peak functions at the origin. |
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| ISSN: | 2227-7390 |