Abstract
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.
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© 2011 Springer-Verlag Berlin Heidelberg
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Diening, L., Harjulehto, P., Hästö, P., Růžička, M. (2011). Classical Operators. 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_6
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DOI: https://doi.org/10.1007/978-3-642-18363-8_6
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18362-1
Online ISBN: 978-3-642-18363-8
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