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Transactions of the American Mathematical Society

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

 

 

Relations between $ H\sp{p}\sb{u}$ and $ L\sp{p}\sb{u}$ with polynomial weights


Authors: Jan-Olov Strömberg and Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 270 (1982), 439-467
MSC: Primary 30D55; Secondary 26C05, 42A50, 46E99
DOI: https://doi.org/10.1090/S0002-9947-1982-0645324-1
MathSciNet review: 645324
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Abstract: Relations between $ L_u^p$ and $ H_u^p$ of the real line are studied in the case when $ p > 1$ and $ u(x) = \vert q(x){\vert^p}w(x)$, where $ q(x)$ is a polynomial and $ w(x)$ satisfies the $ {A_p}$ condition. It turns out that $ H_u^p$ and $ L_u^p$ can be identified when all the zeros of $ q$ are real, and that otherwise $ H_u^p$ can be identified with a certain proper subspace of $ L_u^p$. In either case, a complete description of the distributions in $ H_u^p$ is given. The questions of boundary values and of the existence of dense subsets of smooth functions are also considered.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0645324-1
Article copyright: © Copyright 1982 American Mathematical Society