Trilinear embedding for divergence-form operators with complex coefficientsCarbonaro, Andrea (Avtor) Dragičević, Oliver (Avtor) Kovač, Vjekoslav (Avtor) Škreb, Kristina Ana (Avtor) elliptic differential operatorp-ellipticityoperator semigroupmultilinear estimateWe 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.20232024-03-15 12:10:59Neznano18411UDK: 517.9ISSN pri članku: 0001-8708DOI: 10.1016/j.aim.2023.109239COBISS_ID: 177492995sl