NOTE ON REAL AND IMAGINARY PARTS OF HARMONIC QUASIREGULAR MAPPINGS
Uloženo v:
| Název: | NOTE ON REAL AND IMAGINARY PARTS OF HARMONIC QUASIREGULAR MAPPINGS |
|---|---|
| Autoři: | SUMAN DAS, ANTTI RASILA |
| Zdroj: | Canadian Mathematical Bulletin. :1-10 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Canadian Mathematical Society, 2025. |
| Rok vydání: | 2025 |
| Témata: | Complex Variables, 31A05, 30H10, 30C62, FOS: Mathematics, Complex Variables (math.CV) |
| Popis: | If $f=u+iv$ is analytic in the unit disk $\mathbb{D}$, it is known that the integral means $M_p(r,u)$ and $M_p(r,v)$ have the same order of growth. This is false if $f$ is a (complex-valued) harmonic function. However, we prove that the same principle holds if we assume, in addition, that $f$ is $K$-quasiregular in $\mathbb{D}$. The case $0 9 pages |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 1496-4287 0008-4395 |
| DOI: | 10.4153/s0008439525101240 |
| DOI: | 10.48550/arxiv.2506.04618 |
| Přístupová URL adresa: | http://arxiv.org/abs/2506.04618 |
| Rights: | Cambridge Core User Agreement arXiv Non-Exclusive Distribution |
| Přístupové číslo: | edsair.doi.dedup.....8c33d90da724ea8ef6b041380b687f8c |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | If $f=u+iv$ is analytic in the unit disk $\mathbb{D}$, it is known that the integral means $M_p(r,u)$ and $M_p(r,v)$ have the same order of growth. This is false if $f$ is a (complex-valued) harmonic function. However, we prove that the same principle holds if we assume, in addition, that $f$ is $K$-quasiregular in $\mathbb{D}$. The case $0<br />9 pages |
|---|---|
| ISSN: | 14964287 00084395 |
| DOI: | 10.4153/s0008439525101240 |