A Note on Holomorphic Spaces Defined with the Help of Luzin Cone and Area Integral
The goal of this note is to introduce a new approach to a known problem of finding estimates for ``analytic quazinorms" with Luzin area integral or Luzin cone $\Gamma_\alpha(\xi)$ in them, namely we use new connections between Luzin Area integral and $p$-Carleson measures and apply classical i...
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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2009-01-01
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| Series: | Armenian Journal of Mathematics |
| Online Access: | http://test.armjmath.sci.am/index.php/ajm/article/view/46 |
| Summary: | The goal of this note is to introduce a new approach to a known problem of finding estimates for ``analytic quazinorms" with Luzin area integral or Luzin cone $\Gamma_\alpha(\xi)$ in them, namely we use new connections between Luzin Area integral and $p$-Carleson measures and apply classical interpolation theorems of real analysis to get various new inequalities for analytic functions in the unit disk and polydisk.
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| ISSN: | 1829-1163 |