20.500.12556/DiRROS-18411 Trilinear embedding for divergence-form operators with complex coefficients 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. elliptic differential operator p-ellipticity operator semigroup multilinear estimate true false true Angleški jezik Ni določen Neznano 2024-03-15 12:10:59 2024-03-15 12:10:59 2024-03-16 03:37:15 0000-00-00 00:00:00 2023 0 0 72 str. article no. 109239 Vol. 431 Oct. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-10-01 517.9 0001-8708 10.1016/j.aim.2023.109239 177492995 https://www.sciencedirect.com/science/article/pii/S0001870823003821 1 b4eadd13-e2bc-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25075 1-s2.0-S0001870823003821-main-1.pdf 1-s2.0-S0001870823003821-main-1.pdf 1 8B1845458CDDCA277D057F58DBE69B2E 8638f26dc2d0dcfaa0eefdd8d653076d43568b70bbc46cb9df45e469ce334329 242ee599-e2bd-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25076 Inštitut za matematiko, fiziko in mehaniko 0 0 0