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Afrika Matematika

, Volume 29, Issue 3–4, pp 357–370 | Cite as

On function spaces with S-transform

  • Baby Kalita
  • Sunil Kumar Singh
Article

Abstract

For \(1 \le p,q <\infty \), we define the space \(W^{p,q}_{k_1,k_2}({\mathbb {R}}^n)\) by means of the S-transform where \(k_1\) and \(k_2\) are weight functions on \({{\mathbb {R}}^n}\) and \({\mathbb {R}}^n\times {\mathbb {R}}_0^n \), respectively. It is a Banach space with respect to a sum norm defined in this paper. Latter we discuss inclusion properties and obtain the dual space of \(W^{p,q}_{k_1,k_2}({\mathbb {R}}^n)\). Furthermore, we define the space \(\left( W^{p,q}_{k_1,k_2}\right) _{\xi }({\mathbb {R}}^n)\) where \(\xi \) is fixed and show that it is an essential Banach module over \(L^1_{k_1}({\mathbb {R}}^n)\).

Keywords

S-transform Banach module Multiplier space Weighted lebesgue spaces 

Mathematics Subject Classification

65R10 

Notes

Acknowledgements

The authors are thankful to the referees for their valuable comments and suggestions.

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsRajiv Gandhi UniversityDoimukhIndia
  2. 2.Department of MathematicsMahatma Gandhi Central UniversityMotihariIndia

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