arXiv subjects

Joel Coacalle

Publications and source records attributed to Joel Coacalle.

4 recordsLinked to original sources

arXiv2026

Solvability of elliptic homogeneous linear equations with measure data in weighted Lebesgue spaces

Let $A(D)$ be an elliptic homogeneous linear differential operator with complex constant coefficients, $ μ$ be a vector-valued Borel measure and $w$ be a positive locally integrable function on $\mathbb{R}^N$. In this work, we present sufficient conditions on $μ$ and $w$ for the existence of solutions in the weighted Lebesgue spaces $L^p_w$ for the equation $A^{*}(D)f=μ$, for $ 1\leq p<\infty $. Those conditions are related to a certain control of the Riesz potential of the measure $μ$. We also present sufficient conditions for the solvability when $p=\infty$ adding a canceling condition on the operator. Our method is based on a new weighted $L^1$ Stein-Weiss type inequality on measures for a special class of vector fields.

math.AP↗

arXiv2025

Cancellation conditions and boundedness of Inhomogeneous Calderón-Zygmund operators on local Hardy spaces associate with spaces of homogeneous type

In this work, we present sufficient cancellation conditions for the boundedness of inhomogeneous Calderón-Zygmund type operators on local Hardy spaces defined over spaces of homogeneous type in the sense of Coifman & Weiss for $ 0<p\leq 1 $. A new approach to atoms and molecules for local Hardy spaces in this setting are introduced with special moment conditions.

math.AP↗

arXiv2025

Subelliptic and Maximal $L^p$ Estimates for the Complex Green Operator on non-pseudoconvex domains

We prove subelliptic estimates for ethe complex Green operator $ K_q $ at a specific level $ q $ of the $ \bar\partial_b $-complex, defined on a not necessarily pseudoconvex CR manifold satisfying the commutator finite type condition. Additionally, we obtain maximal $ L^p $ estimates for $ K_q $ by considering closed-range estimates. Our results apply to a family of manifolds that includes a class of weak $ Y(q) $ manifolds satisfying the condition $ D(q) $. We employ a microlocal decomposition and Calderón-Zygmund theory to obtain subelliptic and maximal-$ L^p $ estimates, respectively.

math.CV↗

arXiv2019

Closed range estimates for $\bar\partial_b$ on CR manifolds of hypersurface type

The purpose of this paper is to establish sufficient conditions for closed range estimates on $(0,q)$-forms, for some fixed $q$, $1 \leq q \leq n-1$, for $\bar\partial_b$ in both $L^2$ and $L^2$-Sobolev spaces in embedded, not necessarily pseudoconvex CR manifolds of hypersurface type. The condition, named weak $Y(q)$, is both more general than previously established sufficient conditions and easier to check. Applications of our estimates include estimates for the Szegö projection as well as an argument that the harmonic forms have the same regularity as the complex Green operator. We use a microlocal argument and carefully construct a norm that is well-suited for a microlocal decomposition of form. We do not require that the CR manifold is the boundary of a domain. Finally, we provide an example that demonstrates that weak $Y(q)$ is an easier condition to verify than earlier, less general conditions.

math.CV↗