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Multilinear integral operators in weighted grand Lebesgue spaces

  • Vakhtang Kokilashvili EMAIL logo , Mieczysław Mastyło und Alexander Meskhi
Veröffentlicht/Copyright: 28. Juni 2016
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Abstract

The boundedness of multi(sub)linear Hardy–Littlewood maximal, Calderón–Zygmund and fractional integral operators defined on metric measure spaces is established in weighted grand Lebesgue spaces. In particular, we derive the one-weight inequality for maximal and singular integrals under the Muckenhoupt type conditions, weighted Sobolev type theorem and trace type inequality for fractional integrals.


Dedicated to Professor Stefan G. Samko on the occasion of his 75th anniversary


Acknowledgements

The first and third named authors were partially supported by the Shota Rustaveli National Science Foundation Grant (Contract Numbers: D/13–23 and 31/47). The second named author was supported by National Science Centre, Poland, project no. 2015/17/B/ST1/00064.

The authors are thankful to Prof. V. Kiryakova for remarks and suggestions which made the manuscript better than the initial version.

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Received: 2016-3-1
Published Online: 2016-6-28
Published in Print: 2016-6-1

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