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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$ 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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  • [1] E. Adams, On the identification of weighted Hardy spaces, Indiana Univ. Math. J. 32 (1983), 477-489. MR 703279 (85g:42024)
  • [2] S. Chanillo, J.-O. Strömberg and R. L. Wheeden, Norm inequalities for potential-type operators, Rev. Mat. Iberoamericana (to appear). MR 996820 (90f:42022)
  • [3] B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 34 (1972), 31-38. MR 0311856 (47:418)
  • [4] -, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. MR 0293384 (45:2461)
  • [5] C. Sadosky and R. L. Wheeden, Some weighted norm inequalities for the Fourier transform of functions with vanishing moments, Trans. Amer. Math. Soc. 300 (1987), 521-533. MR 876464 (88c:42027)
  • [6] J.-O. Strömberg and A. Torchinsky, Weighted Hardy spaces, Lecture Notes in Math., Springer (to appear). MR 1011673 (90j:42053)
  • [7] J.-O. Strömberg and R. L. Wheeden, Relations between $ H_u^p$ and $ L_u^p$ with polynomial weights, Trans. Amer. Math. Soc. 270 (1982), 439-467.
  • [8] -, Weighted norm estimates for the Fourier transform with a pair of weights (to appear).

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Article copyright: © Copyright 1989 American Mathematical Society

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