In a recent work by A. Martini and A. Sikora, sharp Lp spectral multiplier theorems for the Grushin operators acting on Rd1x× Rd2x and defined by the formula are obtained in the case d1 ≥d2. Here we complete the picture by proving sharp results in the case d1 < d2. Our approach exploits L2 weighted estimates with -gextra weights-h depending essentially on the second factor of Rd1-Rd2 (in contrast to the mentioned work, where the -gextra weights'h depend only on the first factor) and gives a new unified proof of the sharp results without restrictions on the dimensions.
A sharp multiplier theorem for Grushin operators in arbitrary dimensions / Martini, A.; Muller, D.. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - STAMPA. - 30:4(2014), pp. 1265-1280. [10.4171/rmi/814]
Titolo: | A sharp multiplier theorem for Grushin operators in arbitrary dimensions | |
Autori: | ||
Data di pubblicazione: | 2014 | |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.4171/rmi/814 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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RMI-2014-030-004-06.pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia | |
martinimueller_grushin.pdf | 2. Post-print / Author's Accepted Manuscript | PUBBLICO - Tutti i diritti riservati | Visibile a tuttiVisualizza/Apri |
http://hdl.handle.net/11583/2949512