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October 1995 Directional operators and radial functions on the plane
Javier Duoandikoetxea, Ana Vargas
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Ark. Mat. 33(2): 281-291 (October 1995). DOI: 10.1007/BF02559710

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

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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

Information

Received: 27 June 1994; Published: October 1995
First available in Project Euclid: 31 January 2017

zbMATH: 0852.47014
MathSciNet: MR1373025
Digital Object Identifier: 10.1007/BF02559710

Rights: 1995 © Institut Mittag-Leffler

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Vol.33 • No. 2 • October 1995
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