A condition of Busemann-Feller type for the derivation of integrals of functions in the class Φ (L).
Ireneo Peral Alonso (1977)
Collectanea Mathematica
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Displaying similar documents to “On the derivation and covering properties of a differentiation basis”
A condition of Busemann-Feller type for the derivation of integrals of functions in the class Φ (L).
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We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies a weak type estimate. This allows us to complete Zygmund’s program of the description of the translation invariant bases of multidimensional intervals in the particular case of products of two cubic intervals. As a conjecture, we suggest a more precise version of Zygmund’s program.
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