Armenian Journal of Mathematics, 3(2)
2010; 92–97
Shared with The Gufo

Weighted Sobolev theorem in Lebesgue spaces withvariable exponent: corrigendum

N. Samko*, S. Samko, B. Vakulov

Received: 2024-12-20 · Published: 2010-06-17

© 2010 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
Shared article.
Original title
Weighted Sobolev theorem in Lebesgue spaces withvariable exponent: corrigendum
Authors
N. Samko, S. Samko, B. Vakulov
Source journal
Armenian Journal of Mathematics, 3(2)
Published
2010-06-17
Licence
Creative Commons Attribution 4.0 International
Original
https://armjmath.sci.am/index.php/ajm/article/view/69

Abstract

We fill in a gap discovered in the proof of Theorem A, on weighted Sobolev typeboundedness for potential operators in variable exponent Lebesgue spaces, in the pa-per of the authors ”Weighted Sobolev theorem in Lebesgue spaces with variable expo-nent”, J. Math. Anal. and Applic., 2007, vol. 335, No 1, 560-583. The proof remains thesame in the case where the Matuszewska-Orlich indices푚(푤)and푀(푤)of the weight푤are both positive or negative, but in the case where they have different signs, the proofneeds some additional arguments and requires a slightly different formulation of theresult.
1 / ? 100% Open in new tab Download Cite

Loading the full text…

Download Follow Updates