Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-06T00:18:52.185Z Has data issue: false hasContentIssue false
  • English
  • Français

Weighted estimates for solutions of a Sturm–Liouville equation in the space L1(ℝ)

Published online by Cambridge University Press:  15 November 2011

N. A. Chernyavskaya ,
N. El-Natanov  and
L. A. Shuster
N. A. Chernyavskaya
Affiliation:
Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
N. El-Natanov
Affiliation:
Department of Mathematics, Ariel University Center of Samaria, Ariel 40700, Israel
L. A. Shuster
Affiliation:
Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the equation

where

Under these conditions, (1) is correctly solvable in L1(ℝ), i.e.

(i) for any function f ∈ L1(ℝ), there exists a unique solution of (1), y ∈ L1(ℝ);

(ii) there is an absolute constant c1 ∈ (0, ∞) such that the solution of (1),

In this work we strengthen the a priori inequality (1). We find minimal requirements for a given weight function θ ∈ Lloc1(ℝ) under which the solution of (1), y ∈ L1(ℝ), satisfies the estimate

where c2 is some absolutely positive constant.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 6 , December 2011 , pp. 1175 - 1206
Copyright
Copyright © Royal Society of Edinburgh 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)