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Trilinear embedding for divergence-form operators with complex coefficientsCarbonaro, Andrea ...We prove a dimension-free ▫$L^p(\Omega)\times L^q(\Omega)\times L^r(\Omega)\rightarrow L^1(\Omega\times (0,\infty))$▫ embedding for triples of elliptic operators in divergence form with complex ... coefficients and subject to mixed boundary conditions on ▫$\Omega$▫, and for triples of exponents ▫$p,q,r \in (1,\infty)$▫ mutually related by the identity ▫$1/p+1/q+1/r=1$▫. Here ▫$\Omega$▫ is allowed to be an arbitrary open subset of ▫$\mathbb{R}^d$▫. Our assumptions involving the exponents and coefficient matrices are expressed in terms of a condition known as ▫$p$▫-ellipticity. The proof utilizes the method of Bellman functions and heat flows. As a corollary, we give applications to (i) paraproducts and (ii) square functions associated with the corresponding operator semigroups, moreover, we prove (iii) inequalities of Kato-Ponce type for elliptic operators with complex coefficients. All the above results are the first of their kind for elliptic divergence-form operators with complex coefficients on arbitrary open sets. Furthermore, the approach to (ii),(iii) through trilinear embeddings seems to be new.Source: Advances in mathematics. - ISSN 0001-8708 (Vol. 431, [article no.] 109239, Oct. 2023, 72 str.)Type of material - article, component part ; adult, seriousPublish date - 2023Language - englishCOBISS.SI-ID - 177492995
Author | Carbonaro, Andrea ... |
Title | Trilinear embedding for divergence-form operators with complex coefficients |
Publication date | 2023-08-14 |
COBISS.SI-ID | 177492995 |
Publication version in repository | Publisher's version |
Publication licence | Creative Commons Attribution 4.0 International |
Embargo | Immediate publication for public |
Project(s) from which the publication was funded
Title | Acronym | Project ID | Funder |
---|---|---|---|
p-eliptičnost v harmonični analizi in parcialnih diferencialnih enačbah | J1-1690-2019 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
|
Analiza in geometrija | P1-0291-2022 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
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https://www.sciencedirect.com/science/article/pii/S0001870823003821 |
https://dirros.openscience.si/IzpisGradiva.php?id=18411 |
https://repozitorij.uni-lj.si/IzpisGradiva.php?id=153045 |
source: Advances in mathematics. - ISSN 0001-8708 (Vol. 431, [article no.] 109239, Oct. 2023, 72 str.)
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Carbonaro, Andrea | |
Dragičević, Oliver | 19285 |
Kovač, Vjekoslav | |
Škreb, Kristina Ana |
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