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Beyond Log-Hölder Continuity

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Variable Lebesgue Spaces

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

In this chapter we continue our study of the Hardy-Littlewood maximal operator. In Chap. 3 we showed that the log Hölder continuity conditions LH 0 and LH ∞ are sufficient for the maximal operator to be bounded. In this chapter we will show that they are not necessary, even though they are the best possible pointwise decay conditions. To find weaker sufficient conditions we build upon the proof of Theorem 3.16, which showed that LH 0 and LH ∞ play distinct roles.

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Authors and Affiliations

  1. Department of Mathematics, Trinity College, Hartford, Connecticut, USA

    David V. Cruz-Uribe

  2. Dipartimento di Architettura, Università di Napoli “Federico II”, Napoli, Italy

    Alberto Fiorenza

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  1. David V. Cruz-Uribe
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Cruz-Uribe, D.V., Fiorenza, A. (2013). Beyond Log-Hölder Continuity. In: Variable Lebesgue Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0548-3_4

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