NOTE ON REAL AND IMAGINARY PARTS OF HARMONIC QUASIREGULAR MAPPINGS
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| Title: | NOTE ON REAL AND IMAGINARY PARTS OF HARMONIC QUASIREGULAR MAPPINGS |
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| Authors: | SUMAN DAS, ANTTI RASILA |
| Source: | Canadian Mathematical Bulletin. :1-10 |
| Publication Status: | Preprint |
| Publisher Information: | Canadian Mathematical Society, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Complex Variables, 31A05, 30H10, 30C62, FOS: Mathematics, Complex Variables (math.CV) |
| Description: | 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 |
| Document Type: | Article |
| Language: | English |
| ISSN: | 1496-4287 0008-4395 |
| DOI: | 10.4153/s0008439525101240 |
| DOI: | 10.48550/arxiv.2506.04618 |
| Access URL: | http://arxiv.org/abs/2506.04618 |
| Rights: | Cambridge Core User Agreement arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....8c33d90da724ea8ef6b041380b687f8c |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | 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 |
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| ISSN: | 14964287 00084395 |
| DOI: | 10.4153/s0008439525101240 |