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Linear dimension-free estimates in the embedding theorem for Schrödinger operatorsDragičević, Oliver ; Volberg, AlexanderDokažemo bilinearni vložitveni izrek za Schrödingerjeve operatorje z nenegativnim potencialom. Vložitev, ki deluje na kartezičnem produktu prostora ▫$L^p({\mathbb{R}}^n)$▫ z njegovim dualom, vsebuje ... ocene, ki so neodvisne od dimenzije ▫$n$▫ ter linearne v ▫$p$▫. To dosežemo s pomočjo posebne Bellmanove funkcije, ki zadošča trem ključnim pogojem. Raziščemo tudi povezave z znanimi rezultati na Heisenbergovi grupi kot tudi z rezultati za Hilbertovo transformiranko vzdolž parabole. Verjamemo, da je naš pristop dokaj univerzalen, v smislu, da bi ga bilo moč uporabiti na vrsti Rieszovih transformacij, izhajajočih iz različnih diferencialnih operatorjev.Source: Journal of the London Mathematical Society. - ISSN 0024-6107 (Vol. 85, p. 1, 2012, str. 191-222)Type of material - article, component partPublish date - 2012Language - englishCOBISS.SI-ID - 16214873
Author
Dragičević, Oliver |
Volberg, Alexander
Topics
matematika |
Bellmanova funkcija |
Schrödingerjev operator |
Littlewood-Paleyjeva teorija |
Hermiteov operator |
Rieszove transformacije |
Heisenbergove grupe |
mathematics |
Bellman function |
Schrödinger operator |
Littlewood-Paley theory |
Hermite operator |
Riesz transforms |
Heisenberg groups
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Dragičević, Oliver | 19285 |
Volberg, Alexander | ![]() |
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