| Full text | |
| Author(s): |
Hounie, J.
;
Picon, T.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 494, n. 1, p. 24-pg., 2021-02-01. |
| Abstract | |
Let A (x, D) be an elliptic linear differential operator of order v with smooth complex coefficients in Omega subset of R-N from a complex vector space E to a complex vector space F. In this paper we show that if l is an element of R satisfies 0 < l < N and l <= v, then the estimate (integral(RN) vertical bar Pv-l(x, D)u(x)vertical bar(q)vertical bar x vertical bar(-N+(N-l)q) dx)(1/q) <= C parallel to A(x, D)u parallel to L-1 holds locally for every u is an element of C-c(infinity) (U; E) and 1 <= q < N/(N - l) assuming A(x, D) is canceling, i.e. boolean AND(N)(xi is an element of R) \{0} A(x(0), xi)[E] = {0} for each x(0) is an element of Omega. Here Pv-l(x, D) is a properly supported pseudo-differential operator in Hiirmander's class OpS(1, delta)(v-l)(Omega), 0 <= delta < 1. This statement is inspired in a new characterization of Hardy-Littlewood-Sobolev inequalities for elliptic and canceling homogeneous operators A(D) with constant coefficients that extends and unifies several results stemming from the classical Hardy-Sobolev estimates. Variants and applications are presented with focus on operators associated to elliptic systems of complex vector fields. (C) 2020 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 18/14316-3 - Geometric theory of PDE and multidimensional complex analysis |
| Grantee: | Paulo Domingos Cordaro |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 18/15484-7 - A priori estimates for elliptic operators and applications |
| Grantee: | Tiago Henrique Picon |
| Support Opportunities: | Research Grants - Young Investigators Grants - Phase 2 |