Uniform estimates for local properties of analytic functions in a complete Reinhardt domain
Using recent estimates of maximum modulus for partial derivatives of the analytic functions with bounded $\mathbf{L}$-index in joint variables we describe maximum modulus of these functions at the polydisc skeleton with given radii by the maximum modulus with lesser radii. Such a description is suff...
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| Main Authors: | , |
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| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2024-06-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/520 |
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| Summary: | Using recent estimates of maximum modulus for partial derivatives of the analytic functions with bounded $\mathbf{L}$-index in joint variables we describe maximum modulus of these functions at the polydisc skeleton with given radii by the maximum modulus with lesser radii. Such a description is sufficient and necessary condition of boundedness of $\mathbf{L}$-index in joint variables for functions which are analytic in a complete Reinhardt domain. The vector-valued function $\mathbf{L}$ is a positive and continuous function in the domain and its values at a point is greater than reciprocal of distance from the point to the boundary of the Reinhardt domain multiplied by some constant. |
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| ISSN: | 1027-4634 2411-0620 |