L p eigenfunction bounds for the Hermite operator

Generalized Eigenfunction Expansions for Operator Algebras^)

A generalized eigenfunction expansion may be regarded as a representation for the spectral theorem by a transform technique. These representations have been presented in many forms, an early version of which was the von Neumann "direct integral" decomposition for a class of operator algebras [l9]. In 1953 [17], Mautner applied the von Neumann technique to the class of operators acting in an L2-...

L Bounds for the parabolic singular integral operator

* Correspondence: yanpingch@126. com Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China Full list of author information is available at the end of the article Abstract Let 1 < p <∞ and n ≥ 2. The authors establish the L(R) boundedness for a class of parabolic singular integral operators with rough kernels. MR...

L Bounds for a Maximal Dyadic Sum Operator

The authors prove L bounds in the range 1 < p < ∞ for a maximal dyadic sum operator on R. This maximal operator provides a discrete multidimensional model of Carleson’s operator. Its boundedness is obtained by a simple twist of the proof of Carleson’s theorem given by Lacey and Thiele [6] adapted in higher dimensions [8]. In dimension one, the L boundedness of this maximal dyadic sum implies in...

Schwartz functions, Hermite functions, and the Hermite operator

On the Localization Eigenfunction Expansions Associated with the Schrodinger Operator

In this paper we study eigenfunction expansions associated with the Schrodinger operator with a singular potential. In the paper it is obtained sufficient conditions for localization and uniformly convergence of the regularizations of the corresponding expansions