Abstract
LetEçS 1 be a set with Minkowski dimensiond(E)1. We consider the Hardy-Littlewood maximal function, the Hilbert transform and the maximal Hilbert transform along the directions ofE. The main result of this paper shows that these operators are bounded onL p rad (R2) forp>1+d(E) and unbounded whenp<1+d(E). We also give some end-point results.
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Both authors are partially supported by Spanish DGICYT grant no. PB90-0187
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Duoandikoetxea, J., Vargas, A. Directional operators and radial functions on the plane. Ark. Mat. 33, 281–291 (1995). https://doi.org/10.1007/BF02559710
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DOI: https://doi.org/10.1007/BF02559710