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Scientific paper - Original scientific paper
Trilinear embedding for divergence-form operators with complex coefficients
Advances in mathematics, 431 (2023); 1-72. https://doi.org/10.1016/j.aim.2023.109239
Carbonaro, Andrea; Dragičević, Oliver; Kovač, Vjekoslav; Škreb, Kristina Ana

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Carbonaro, A., Dragičević, O., Kovač, V. & Škreb, K. A. (2023). Trilinear embedding for divergence-form operators with complex coefficients. Advances in mathematics, 431., 1-72. doi: 10.1016/j.aim.2023.109239

Carbonaro, Andrea, et al. "Trilinear embedding for divergence-form operators with complex coefficients." Advances in mathematics, vol. 431, 2023, pp. 1-72. https://doi.org/10.1016/j.aim.2023.109239

Carbonaro, Andrea, Oliver Dragičević, Vjekoslav Kovač and Kristina Ana Škreb. "Trilinear embedding for divergence-form operators with complex coefficients." Advances in mathematics 431 (2023): 1-72. https://doi.org/10.1016/j.aim.2023.109239

Carbonaro, A., et al. (2023) 'Trilinear embedding for divergence-form operators with complex coefficients', Advances in mathematics, 431, pp. 1-72. doi: 10.1016/j.aim.2023.109239

Carbonaro A, Dragičević O, Kovač V, Škreb KA. Trilinear embedding for divergence-form operators with complex coefficients. Advances in mathematics [Internet]. 2023 [cited 2024 November 23];431:1-72. doi: 10.1016/j.aim.2023.109239

A. Carbonaro, O. Dragičević, V. Kovač and K. A. Škreb, "Trilinear embedding for divergence-form operators with complex coefficients", Advances in mathematics, vol. 431, pp. 1-72, 2023. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:237:376950. [Accessed: 23 November 2024]

Metadata
Title (english)Trilinear embedding for divergence-form operators with complex coefficients
AuthorAndrea Carbonaro
AuthorOliver Dragičević
AuthorVjekoslav Kovač
AuthorKristina Ana Škreb
Author's institutionUniversity of Zagreb
Faculty of Civil Engineering
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract (english)
We prove a dimension-free Lp(Ω)×Lq(Ω)×Lr(Ω)→L1(Ω×(0,∞)) embedding for triples of elliptic operators in divergence form with complex coefficients and subject to mixed boundary conditions on Ω, and for triples of exponents p,q,r∈(1,∞) mutually related by the identity 1/p+1/q+1/r=1. Here Ω is allowed to be an arbitrary open subset of Rd. 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.
Keywords (english)
Languageenglish
Publication typeScientific paper - Original scientific paper
Publication statusPublished
Peer reviewPeer review - international
Publication versionPublished version
Journal titleAdvances in mathematics
Numberingvol. 431, pp. 1-72
e-ISSN1090-2082
DOIhttps://doi.org/10.1016/j.aim.2023.109239
URN:NBNurn:nbn:hr:237:376950
Publication2023
Type of resourceText
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-09-05 06:58:13