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

Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spaces Abstract New function spaces L p ( · ) , θ $L^{ p(\,\cdot \,), \theta }$ , ℒ p ( · ) , θ ${\mathcal {L}}^{ p(\,\cdot \,), \theta }$ 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 L p ( · ) , θ $L^{ p(\,\cdot \,),\theta }$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

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

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Publisher
de Gruyter
Copyright
Copyright © 2014 by the
ISSN
1072-947X
eISSN
1572-9176
DOI
10.1515/gmj-2014-0047
Publisher site
See Article on Publisher Site

Abstract

Abstract New function spaces L p ( · ) , θ $L^{ p(\,\cdot \,), \theta }$ , ℒ p ( · ) , θ ${\mathcal {L}}^{ p(\,\cdot \,), \theta }$ 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 L p ( · ) , θ $L^{ p(\,\cdot \,),\theta }$ .

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2014

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