Estimate of K-functionals and modulus of smoothness constructed by generalized spherical mean operator

Using a generalized spherical mean operator, we define generalized modu-lus of smoothness in the space L k 2 ( ℝ d ) . Based on the Dunkl operator we define Sobolev-type space and K -functionals. The main result of the paper is the proof of the equivalence theorem for a K -functional and a modulus o...

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Bibliographic Details
Published inProceedings of the Indian Academy of Sciences. Mathematical sciences Vol. 124; no. 2; pp. 235 - 242
Main Authors HAMMA, M EL, DAHER, R
Format Journal Article
LanguageEnglish
Published India Springer India 01.05.2014
Subjects
Mathematics
Mathematics and Statistics
functional
33C67
47B48
33C52
modulus of smoothness
Dunkl operator
generalized spherical mean operator
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Summary:Using a generalized spherical mean operator, we define generalized modu-lus of smoothness in the space L k 2 ( ℝ d ) . Based on the Dunkl operator we define Sobolev-type space and K -functionals. The main result of the paper is the proof of the equivalence theorem for a K -functional and a modulus of smoothness for the Dunkl transform on ℝ d .
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-014-0173-8