Related papers: On Analytic Solvability and Hypoellipticity For $\…
By using some recent results for divergence form equations, we study the $L_p$-solvability of second-order elliptic and parabolic equations in nondivergence form for any $p\in (1,\infty)$. The leading coefficients are assumed to be in…
We consider the linearized Landau operator for which we provide simple proofs of hypoellipticity, and in particular we recover the recent results of H\' erau and Pravda-Starov \cite{herau-all}. Our arguments are elementary and in particular…
We obtain some L2 results for d-bar on forms that vanish to high order on the singular set of a complex space. As a consequence of our main theorem we obtain weighted L2-solvability results for compactly supported d-bar closed (p,q) forms…
The sharp Gevrey hypoellipticity is provided for the following generalization of the M\'etivier operator, "Non-hypoellipticit\'e analytique pour $D_{x}^{2}+\left( x^{2} + y^{2}\right)D_{y}^{2}$" by G. M\'etivier, \begin{align*}…
Let $X$ be an analytic space of pure dimension. We introduce a formalism to generate intrinsic weighted Koppelman formulas on $X$ that provide solutions to the $\dbar$-equation. We obtain new existence results for the $\dbar$-equation, as…
For a domain $D$ of $\mathbb{C}^n$ which is weakly $q$-pseudoconvex or $q$-pseudoconcave we give a sufficient condition for subelliptic estimates for the $\bar{\partial}$-Neumann problem. The paper extends to domains which are not…
In the first part we analyze space $\mathcal G^*(\mathbb R^{n}_+)$ and its dual through Laguerre expansions when these spaces correspond to a general sequence $\{M_p\}_{p\in\mathbb N_0}$, where $^*$ is a common notation for the Beurling and…
The work deals with the studies of the existence of solutions of an integro-differential equation in the situation of the difference of the standard Laplacian and the bi-Laplacian in the diffusion term. The proof of the existence of…
We discuss the polar in symbol space to hypoelliptic and partially hypoelliptic operators, assuming a transmission property related to a rectifiable boundary and using a representation based on two scalar products.
The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced in "Analytic Hypoellipticity for Sums of Squares and the Treves Conjecture" by P. Albano and A. Bove and M.…
This paper has been withdrawn, and is replaced with paper "Solvability of elliptic systems with square integrable boundary data" by the same authors.
We obtain subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces embedded in $\mathbb{C}^n$ with isolated singularities. $W^{\epsilon}$ Sobolev norms of a form, $f$, for $0< \epsilon < 1$ are estimated in terms…
This paper provides a complete characterization of global hypoellipticity and solvability with loss of derivatives for Fourier multiplier operators on the $n$-dimensional torus. We establish necessary and sufficient conditions for these…
We show subellipticity of the d-bar Neumann problem on domains with Lipschitz boundary in the presence of plurisubharmonic functions with Hessians of algebraic growth. In particular, a subelliptic estimate holds near a point where the…
In an interesting note, E.M. Stein observed some 20 years ago that while the Kohn Laplacian $\square_b$ on functions is neither locally solvable nor (analytic) hypoelliptic, the addition of a non-zero complex constant reversed these…
We prove an abstract theorem of maximal hypoellipticy showing that in an abstract calculus under some natural assumptions, an operator is maximally hypoelliptic if and only if its principal symbol is left invertible. We then show that our…
This paper presents a class of domains on which the Kohn Laplacian and the dib-bar-Neumann problem are hypoelliptic but not superlogarithmic and which, moreover, have a set of points of Levi-degeneracy with positive CR dimension.
We give a semiclassical analysis of a nonlinear eigenvalue problem arising from the study of the failure of analytic hypoellipticity and obtain a general family of hypoelliptic, but not analytic hypoelliptic operators.
We study a complex valued version of the Sobolev inequalities and its relationship to compactness of the d-bar-Neumann operator. For this purpose we use an abstract characterization of compactness derived from a general description of…
The main objective of this paper is twofold. We first show that if the doubly-weighted Bohr spectrum of an almost periodic function exists, then it is either empty or coincides with the Bohr spectrum of that function. Next, we investigate…