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Volume 2, Issue 3, Article 37 |
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$L^p-$Improving Properties for Measures on $\mathbb{R}^{4}$ Supported on Homogeneous Surfaces in Some Non Elliptic Cases
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Authors: |
E. Ferreyra, T. Godoy, M. Urciuolo, |
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Keywords:
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Singular Measures, $L^p$-Improving, Convolution Operators. |
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Date Received:
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08/01/01 |
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Date Accepted:
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05/06/01 |
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Subject Codes: |
42B20,42B10.
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Editors: |
Lubos Pick, |
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Abstract: |
In this paper we study convolution operators  with measures  in  of the form  where  is the unit ball of  , and  is a homogeneous polynomial function. If  vanishes only on a finite union of lines, we prove that is bounded from  into  if  belongs to certain explicitly described trapezoidal region.
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