20.500.12556/RUL-153045 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 Bellman function heat flow true false true Angleški jezik Ni določen Članek v reviji 2023-12-15 08:50:56 2023-12-15 08:51:00 2023-12-16 03:49:04 0000-00-00 00:00:00 2023 0 0 72 str. art. 109239 Vol. 431 Oct. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.9 0001-8708 10.1016/j.aim.2023.109239 177492995 1-s2.0-S0001870823003821-main.pdf 1-s2.0-S0001870823003821-main.pdf 1 872C86FBAE06E29E62ACA27EA4B33BE1 eb26cd62e42cc76fbe0def95b007dfb216a920906d9d2444637210b7710841bf 1e2b68bf-9b1f-11ee-bebf-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=178836 https://www.sciencedirect.com/science/article/pii/S0001870823003821 1 b06d18e2-9b1e-11ee-bebf-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=178835 Fakulteta za matematiko in fiziko 0 0 0