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Corrections to the paper 'The boundedness of certain sublinear operator in the weighted variable Lebesgue spaces'
- Source :
- Czechoslovak Mathematical Journal. 63:1149-1152
- Publication Year :
- 2013
- Publisher :
- Institute of Mathematics, Czech Academy of Sciences, 2013.
-
Abstract
- In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space. Note that the proof of multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent don't contained any mistakes. But at the proving of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in this paper. This result is assigned as Theorem 5 in noted paper. In other words, sufficient conditions for general weights ensuring the validity of the two-weight strong type inequalities for some sublinear operator was found. In this theorem the inequality (9) isn't true. In this note we give the details of the correct argument. We presume that the reader is familiar with the contents and notation of our original paper. At the heart of our correction is the following Theorem which replaces Theorem 5.
- Subjects :
- Discrete mathematics
Mathematics::Functional Analysis
Sublinear function
General Mathematics
Mathematics::Classical Analysis and ODEs
Lebesgue's number lemma
Type (model theory)
symbols.namesake
Operator (computer programming)
Mathematics - Classical Analysis and ODEs
Ordinary differential equation
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
symbols
Standard probability space
Lp space
Variable (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 15729141 and 00114642
- Volume :
- 63
- Database :
- OpenAIRE
- Journal :
- Czechoslovak Mathematical Journal
- Accession number :
- edsair.doi.dedup.....03414eea51c2fcf858789bb4cd6a8847