Abstract
LetEçS1 be a set with Minkowski dimension d(E)1. We consider the Hardy-Littlewood maximal function, the Hilbert transform and the maximal Hilbert transform along the directions of E. The main result of this paper shows that these operators are bounded on L ${}_{rad}^{p}$ (R2) for p>1+d(E) and unbounded when p<1+d(E). We also give some end-point results.
Funding Statement
Both authors are partially supported by Spanish DGICYT grant no. PB90-0187
Citation
Javier Duoandikoetxea. Ana Vargas. "Directional operators and radial functions on the plane." Ark. Mat. 33 (2) 281 - 291, October 1995. https://doi.org/10.1007/BF02559710
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