Relations between and 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

DOI:
https://doi.org/10.1090/S0002-9947-1989-0951891-7

MathSciNet review:
951891

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Abstract: Relations between and are studied for the product space in the case and , where and are polynomials and satisfies the condition for rectangles. A description of the distributions in is given. Questions about boundary values and about the existence of dense subsets of smooth functions satisfying appropriate moment conditions are also considered.

**[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**and**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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DOI:
https://doi.org/10.1090/S0002-9947-1989-0951891-7

Article copyright:
© Copyright 1989
American Mathematical Society