What is a Sobolev space for the Laguerre function systems?

B. Bongioanni, and J. L. Torrea. "What is a Sobolev space for the Laguerre function systems?." Studia Mathematica 192.2 (2009): 147-172. <http://eudml.org/doc/284684>.

@article{B2009,
abstract = {We discuss the concept of Sobolev space associated to the Laguerre operator $L_\{α\} = - y d²/dy² - d/dy + y/4 + α²/4y$, y ∈ (0,∞). We show that the natural definition does not agree with the concept of potential space defined via the potentials $(L_\{α\})^\{-s\}$. An appropriate Laguerre-Sobolev space is defined in order to achieve that coincidence. An application is given to the almost everywhere convergence of solutions of the Schrödinger equation. Other Laguerre operators are also considered.},
author = {B. Bongioanni, J. L. Torrea},
journal = {Studia Mathematica},
keywords = {Laguerre functions; Sobolev spaces; Riesz transforms},
language = {eng},
number = {2},
pages = {147-172},
title = {What is a Sobolev space for the Laguerre function systems?},
url = {http://eudml.org/doc/284684},
volume = {192},
year = {2009},
}

TY - JOUR
AU - B. Bongioanni
AU - J. L. Torrea
TI - What is a Sobolev space for the Laguerre function systems?
JO - Studia Mathematica
PY - 2009
VL - 192
IS - 2
SP - 147
EP - 172
AB - We discuss the concept of Sobolev space associated to the Laguerre operator $L_{α} = - y d²/dy² - d/dy + y/4 + α²/4y$, y ∈ (0,∞). We show that the natural definition does not agree with the concept of potential space defined via the potentials $(L_{α})^{-s}$. An appropriate Laguerre-Sobolev space is defined in order to achieve that coincidence. An application is given to the almost everywhere convergence of solutions of the Schrödinger equation. Other Laguerre operators are also considered.
LA - eng
KW - Laguerre functions; Sobolev spaces; Riesz transforms
UR - http://eudml.org/doc/284684
ER -