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Published in:
2011 | OriginalPaper | Chapter
Classical Operators
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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In this section we treat some of the most important operators of harmonic analysis in a variable exponent context. The results build on the boundedness of the maximal operator. We treat the Riesz potential operator, the sharp maximal function and singular integral operators in the three sections of the chapter. Several further operators are considered in Sect. 7.2. These results are applied in the second part of the book for instance to prove Sobolev embeddings and in the third part to prove existence and regularity of solutions to certain PDEs.