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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Anisotropic $ H\sp{p}$ real interpolation, and fractional Riesz potentials


Author: W. R. Madych
Journal: Trans. Amer. Math. Soc. 232 (1977), 255-263
MSC: Primary 46E35
DOI: https://doi.org/10.1090/S0002-9947-1977-0450961-1
MathSciNet review: 0450961
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Abstract: We observe that the anisotropic variants of $ {H^p}$ interpolate by the real method in the usual manner. Using this fact we show that the corresponding fractional Riesz potentials and related operators perform an embedding in $ {H^p},p > 0$, analogous to the one for $ {L^p},p > 1$. We also state a theorem concerning the mapping properties of $ f \to h \ast f$, where h is in $ B_\alpha ^{1,\infty }$, which hold only for a restricted range of p.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0450961-1
Article copyright: © Copyright 1977 American Mathematical Society