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Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spaces

  • Vakhtang Kokilashvili EMAIL logo and Alexander Meskhi
Published/Copyright: November 6, 2014
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Abstract

New function spaces Lp(·),θ, p(·),θ unifying grand Lebesgue spaces and variable exponent Lebesgue spaces are introduced. The boundedness of maximal and Calderón–Zygmund operators in these spaces defined on spaces of homogeneous type are derived. The Sobolev type theorem for fractional integrals is also established in the class of functions which is narrower than the space Lp(·),θ.

Funding source: Shota Rustaveli National Science Foundation

Award Identifier / Grant number: D/13-23

Funding source: Shota Rustaveli National Science Foundation

Award Identifier / Grant number: 31/47

Received: 2014-1-8
Accepted: 2014-3-11
Published Online: 2014-11-6
Published in Print: 2014-12-1

© 2014 by De Gruyter

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