2011 | OriginalPaper | Chapter
The Generalized Muckenhoupt Condition*
Authors : Lars Diening, Petteri Harjulehto, Peter Hästö, Michael Růžička
Published in: Lebesgue and Sobolev Spaces with Variable Exponents
Publisher: Springer Berlin Heidelberg
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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.