## Arkiv för Matematik

• Ark. Mat.
• Volume 33, Number 2 (1995), 281-291.

### Directional operators and radial functions on the plane

#### 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.

#### Note

Both authors are partially supported by Spanish DGICYT grant no. PB90-0187

#### Article information

Source
Ark. Mat., Volume 33, Number 2 (1995), 281-291.

Dates
First available in Project Euclid: 31 January 2017

https://projecteuclid.org/euclid.afm/1485898472

Digital Object Identifier
doi:10.1007/BF02559710

Mathematical Reviews number (MathSciNet)
MR1373025

Zentralblatt MATH identifier
0852.47014

Rights

#### Citation

Duoandikoetxea, Javier; Vargas, Ana. Directional operators and radial functions on the plane. Ark. Mat. 33 (1995), no. 2, 281--291. doi:10.1007/BF02559710. https://projecteuclid.org/euclid.afm/1485898472

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