Abstract
The boundedness of the maximal operator M is closely linked to very impor tant properties of the spaces \(L^{p(.)}\). Indeed, we will see in Chaps. 6 and 8 that the boundedness ofM is needed for the Sobolev embeddings\(W^{1,p^{(.)}}\hookrightarrow L^{p^{*(.)}}\) , boundedness singular integrals on \(L^{p(.)}\) and Korn’s inequality.
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© 2011 Springer-Verlag Berlin Heidelberg
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Diening, L., Harjulehto, P., Hästö, P., Růžička, M. (2011). The Generalized Muckenhoupt Condition* . In: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics(), vol 2017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18363-8_5
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DOI: https://doi.org/10.1007/978-3-642-18363-8_5
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Online ISBN: 978-3-642-18363-8
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