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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Strong type endpoint bounds for analytic families of fractional integrals


Author: Loukas Grafakos
Journal: Proc. Amer. Math. Soc. 117 (1993), 653-663
MSC: Primary 42B20
DOI: https://doi.org/10.1090/S0002-9939-1993-1100652-3
MathSciNet review: 1100652
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Abstract: In $ {\mathbb{R}^2}$ we consider an analytic family of fractional integrals, whose convolution kernel is obtained by taking some transverse derivatives of arclength measure on the parabola $ (t,{t^2})$ multiplied by $ \vert t{\vert^\gamma }$ and doing so in a homogeneous way. We determine the exact range of $ p,\;q$ for which the analytic family maps $ {L^p}$ to $ {L^q}$. We also resolve a similar issue on the Heisenberg group.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1100652-3
Article copyright: © Copyright 1993 American Mathematical Society

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