Relations between and 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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Relations between and of the real line are studied in the case when and , where is a polynomial and satisfies the condition. It turns out that and can be identified when all the zeros of are real, and that otherwise can be identified with a certain proper subspace of . In either case, a complete description of the distributions in is given. The questions of boundary values and of the existence of dense subsets of smooth functions are also considered.

**[1]**E. Adams,*On weighted norm inequalities for the Hilbert transform of functions with moments zero*, Trans. Amer. Math. Soc. (to appear). MR**662048 (83m:44002)****[2]**A. P. Calderón and A. Zygmund,*Local properties of solutions of elliptic partial differential equations*, Studia Math.**20**(1961), 171-225. MR**0136849 (25:310)****[3]**R. F. Gundy and R. L. Wheeden,*Weighted integral inequalities for the non-tangential maximal function, Lusin area integral, and Walsh-Paley series*, Studia Math.**49**(1974), 107-124. MR**0352854 (50:5340)****[4]**R. A. Hunt, B. Muckenhoupt and R. L. Wheeden,*Weighted norm inequalities for the conjugate function and Hilbert transform*, Trans. Amer. Math. Soc.**176**(1973), 227-251. MR**0312139 (47:701)****[5]**B. Muckenhoupt,*Hardy's inequality with weights*, Studia Math.**44**(1972), 31-38. MR**0311856 (47:418)****[6]**-,*Weighted norm inequalities for the Hardy maximal function*, Trans. Amer. Math. Soc.**165**(1972), 207-226. MR**0293384 (45:2461)****[7]**B. Muckenhoupt, W.-S. Young and R. L. Wheeden,*multipliers with power weights*, Adv. in Math. (to appear). MR**714588 (85d:42010)****[8]**-,*multipliers with polynomial weights*(to appear).**[9]**J.-O. Strömberg and A. Torchinsky,*Weighted Hardy spaces*(to appear).

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
30D55,
26C05,
42A50,
46E99

Retrieve articles in all journals with MSC: 30D55, 26C05, 42A50, 46E99

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0645324-1

Article copyright:
© Copyright 1982
American Mathematical Society