| Title: | Trilinear embedding for divergence-form operators with complex coefficients |
|---|
| Authors: | ID Carbonaro, Andrea (Author)
ID Dragičević, Oliver (Author)
ID Kovač, Vjekoslav (Author)
ID Škreb, Kristina Ana (Author) |
|---|
| Files: |  URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0001870823003821
 PDF - Presentation file, download (1,10 MB)
MD5: 8B1845458CDDCA277D057F58DBE69B2E
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | elliptic differential operator, p-ellipticity, operator semigroup, multilinear estimate |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.10.2023 |
|---|
| Year of publishing: | 2023 |
|---|
| Number of pages: | 72 str. |
|---|
| Numbering: | Vol. 431, article no. 109239 |
|---|
| PID: | 20.500.12556/DiRROS-18411  |
|---|
| UDC: | 517.9 |
|---|
| ISSN on article: | 0001-8708 |
|---|
| DOI: | 10.1016/j.aim.2023.109239 |
|---|
| COBISS.SI-ID: | 177492995 |
|---|
| Note: |
|
|---|
| Publication date in DiRROS: | 15.03.2024 |
|---|
| Views: | 456 |
|---|
| Downloads: | 235 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
