Lp boundedness of Riesz transform related to Schroedinger operators on a manifold
نویسندگان
چکیده
منابع مشابه
L Boundedness of Riesz transform related to Schrödinger operators on a manifold
We establish various Lp estimates for the Schrödinger operator −∆ + V on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where ∆ is the Laplace-Beltrami operator and V belongs to a reverse Hölder class. At the end of this paper we apply our result on Lie groups with polynomial growth.
متن کاملBoundedness for Riesz transform associated with Schrödinger operators and its commutator on weighted Morrey spaces related to certain nonnegative potentials
*Correspondence: [email protected] School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China Abstract Let L = – + V be a Schrödinger operator, where is the Laplacian on Rn and the nonnegative potential V belongs to the reverse Hölder class Bq for q≥ n/2. The Riesz transform associated with the operator L is denoted by T =∇(– + V)– 2 and the dual Ri...
متن کاملLp(R) BOUNDEDNESS AND COMPACTNESS OF LOCALIZATION OPERATORS ASSOCIATED WITH THE STOCKWELL TRANSFORM
In this article, we prove the boundedness and compactness of localization operators associated with Stockwell transforms, which depend on a symbol and two windows, on Lp(R), 1 ≤ p ≤ ∞.
متن کاملON THE Lp BOUNDEDNESS OF WAVE OPERATORS FOR TWO-DIMENSIONAL SCHRÖDINGER OPERATORS WITH THRESHOLD OBSTRUCTIONS
Let H = −∆ + V be a Schrödinger operator on L(R) with real-valued potential V , and let H0 = −∆. If V has sufficient pointwise decay, the wave operators W± = s − limt→±∞ eitHe−itH0 are known to be bounded on L(R) for all 1 < p < ∞ if zero is not an eigenvalue or resonance. We show that if there is an s-wave resonance or an eigenvalue only at zero, then the wave operators are bounded on L(R) for...
متن کاملControl for Schroedinger operators on tori
A well known result of Jaffard states that an arbitrary region on a torus controls , in the L 2 sense, solutions of the free stationary and dynamical Schrödinger equations. In this note we show that the same result is valid in the presence of a potential, that is for Schrödinger operators, −∆ + V , V ∈ C ∞ .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2009
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.2009.4.05