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Transactions of the American Mathematical Society
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$ in a product space


Authors: Jan-Olov Strömberg and Richard L. Wheeden
Journal: Trans. Amer. Math. Soc. 315 (1989), 769-797
MSC: Primary 46E15; Secondary 42B30
MathSciNet review: 951891
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Abstract: Relations between $ L_u^p$ and $ H_u^p$ are studied for the product space $ {{\mathbf{R}}^1} \times {{\mathbf{R}}^1}$ in the case $ 1 < p < \infty$ and $ u({x_1},{x_2}) = \vert{Q_1}({x_1}){\vert^p}\vert{Q_2}({x_2}){\vert^p}w({x_1},{x_2})$, where $ {Q_1}$ and $ {Q_2}$ are polynomials and $ w$ satisfies the $ {A_p}$ condition for rectangles. A description of the distributions in $ H_u^p$ is given. Questions about boundary values and about the existence of dense subsets of smooth functions satisfying appropriate moment conditions are also considered.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0951891-7
PII: S 0002-9947(1989)0951891-7
Article copyright: © Copyright 1989 American Mathematical Society