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Smooth and Nonsmooth Calderón-Zygmund Type Decompositions for Morrey Spaces

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Abstract

It is shown that it is possible to construct an analogue of the Calderón-Zygmund decomposition for the Morrey spaces Morλ for the entire interval λ ∈ (0,1]. Moreover, for λ ∈ (1-,1] it is possible to construct a smooth analogue of the Calderón-Zygmund decomposition. The reason why we do not have any smooth analogues for the entire interval λ ∈ (0,1] is related to the following interesting property of cubes in the Whitney decomposition lemma: The sum of the volumes of Whitney cubes to the power λ is equal to infinity for λ ∈ (0,1-(1/n)].

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  1. Department of Mathematics, Luleå University of Technology, Luleå SE-971 87, Sweden

    N. Kruglyak & E. A. Kuznetsov

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  1. N. Kruglyak
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  2. E. A. Kuznetsov
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Correspondence to N. Kruglyak or E. A. Kuznetsov.

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Kruglyak, N., Kuznetsov, E. Smooth and Nonsmooth Calderón-Zygmund Type Decompositions for Morrey Spaces. J Fourier Anal Appl 11, 697–714 (2005). https://doi.org/10.1007/s00041-005-5032-7

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  • DOI: https://doi.org/10.1007/s00041-005-5032-7

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