Multiple vector-valued, mixed norm estimates for Littlewood-Paley square functions
Benea, Cristina (Université de Nantes. Laboratoire Jean Leray)
Muscalu, Camil (Cornell University. Department of Mathematics)

Date:	2022
Abstract:	We prove that for any LQ-valued Schwartz function f defined on Rd, one has the multiple vector-valued, mixed-norm estimate kfkLP (LQ) . kSfkLP (LQ) valid for every d-tuple P and every n-tuple Q satisfying 0 < P, Q < ∞ componentwise. Here S := Sd1 ⊗ · · · ⊗ SdN is a tensor product of several Littlewood-Paley square functions Sdj defined on arbitrary Euclidean spaces R dj for 1 ≤ j ≤ N, with the property that d1 + · · · + dN = d. This answers a question that came up implicitly in our recent works [2], [3], [5] and completes in a natural way classical results of Littlewood-Paley theory. The proof is based on the helicoidal method introduced by the authors in the aforementioned papers.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Multi-parameter littlewood-paley theory ; Multi-parameter hardy spaces ; Mixed-norm estimates ; Weighted estimates and littlewood-paley theory
Published in:	Publicacions matemàtiques, Vol. 66 Núm. 2 (2022) , p. 631-681 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/402239
DOI: 10.5565/PUBLMAT6622205

51 p, 594.2 KB

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