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  • Trilinear embedding for divergence-form operators with complex coefficients
    Carbonaro, 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.
    Vir: Advances in mathematics. - ISSN 0001-8708 (Vol. 431, [article no.] 109239, Oct. 2023, 72 str.)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2023
    Jezik - angleški
    COBISS.SI-ID - 177492995

    Povezava(-e):

    https://www.sciencedirect.com/science/article/pii/S0001870823003821
    DiRROS - Digitalni repozitorij raziskovalnih organizacij Slovenije
    Repozitorij Univerze v Ljubljani – RUL
    DOI

vir: Advances in mathematics. - ISSN 0001-8708 (Vol. 431, [article no.] 109239, Oct. 2023, 72 str.)
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