H∞-calculus for Hypoelliptic Pseudodifferential Operators
نویسنده
چکیده
We establish the existence of a bounded H∞-calculus for a large class of hypoelliptic pseudodifferential operators on R and closed manifolds.
منابع مشابه
properties of M−hyoellipticity for pseudo differential operators
In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...
متن کاملThe Atiyah-Singer Index Formula for Subelliptic Operators on Contact Manifolds, Part II
We present a new solution to the index problem for hypoelliptic operators in the Heisenberg calculus on contact manifolds, by constructing the appropriate topological K-theory cocycle for such operators. Its Chern character gives a cohomology class to which the Atiyah-Singer index formula can be applied. Such a K-cocycle has already been constructed by Boutet de Monvel for Toeplitz operators, a...
متن کاملBounded H∞-calculus for Pseudodifferential Operators and Applications to the Dirichlet-neumann Operator
Operators of the form A = a(x,D) +K with a pseudodifferential symbol a(x, ξ) belonging to the Hörmander class Sm 1,δ, m > 0, 0 ≤ δ < 1, and certain perturbations K are shown to possess a bounded H∞-calculus in Besov-Triebel-Lizorkin and certain subspaces of Hölder spaces, provided a is suitably elliptic. Applications concern pseudodifferential operators with mildly regular symbols and operators...
متن کاملNoncommutative Residue for Heisenberg Manifolds. I.
In this paper we construct a noncommutative residue for the Heisenberg calculus, that is, for the hypoelliptic calculus on Heisenberg man-ifolds, including on CR and contact manifolds. This noncommutative residue as the residual induced on operators of integer orders by the analytic extension of the usual trace to operators of non-integer orders and it agrees with the integral of the density de...
متن کاملSobolev Space Estimates and Symbolic Calculus for Bilinear Pseudodifferential Operators
Bilinear operators are investigated in the context of Sobolev spaces and various techniques useful in the study of their boundedness properties are developed. In particular, several classes of symbols for bilinear operators beyond the so called CoifmanMeyer class are considered. Some of the Sobolev space estimates obtained apply to both the bilinear Hilbert transform and its singular multiplier...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009