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A rotation method which gives linear ▫$L^p$▫ estimates for powers of the Ahlfors-Beurling operatorDragičević, Oliver ; Petermichl, Stefanie ; Volberg, AlexanderV članku [O. Dragičević, A. Volberg, Sharp estimate of the Ahlfors-Beurling operator via averaging martingale transforms, Michigan Math. J. 51 (2) (2003) 415-435] je bil Ahlfors-Beurlingov operator ... ▫$T$▫ predstavljen kot povprečje dvodimenzionalnih martingalskih transformacij. Izkaže se, da isti rezultat velja tudi za ▫$T^n$▫. Motivirani z [T. Iwaniec, G. Martin, Riesz transforms and related singular integrals, J. Reine Angew. Math. 473 (1996) 25-57] odtod izpeljemo, da so ▫$\Vert T^n \Vert_p$▫ navzgor omejene z ▫$Cnp^\ast$, $p^\ast = \max\{p,\frac{p}{p-1}\}$▫. To oceno še izboljšamo in opišemo optimalno obnašanje obravnavanih ▫$L^p$▫ norm.Source: Journal de Mathématiques Pures et Appliquées. - ISSN 0021-7824 (Vol. 86, iss. 6, 2006, str. 492-509)Type of material - article, component partPublish date - 2006Language - englishCOBISS.SI-ID - 14157657
Author
Dragičević, Oliver |
Petermichl, Stefanie |
Volberg, Alexander
Topics
matematika |
Ahlfors-Beurlingov operator |
Haarovi sistemi |
rotacijska metoda |
Burkholderjev lema o diferencialni podrejenosti |
mathematics |
Ahlfors-Beurling operator |
Haar systems |
method of rotations |
Burkholder's differential subordination lemma
source: Journal de Mathématiques Pures et Appliquées. - ISSN 0021-7824 (Vol. 86, iss. 6, 2006, str. 492-509)
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Dragičević, Oliver | 19285 |
Petermichl, Stefanie | |
Volberg, Alexander |
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