A two weight weak type inequality for fractional integrals

Author:
Eric Sawyer

Journal:
Trans. Amer. Math. Soc. **281** (1984), 339-345

MSC:
Primary 26A33; Secondary 26D10, 26D15, 42B25

DOI:
https://doi.org/10.1090/S0002-9947-1984-0719674-6

MathSciNet review:
719674

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For and nonnegative weight functions on we show that the weak type inequality

**[1]**D. R. Adams,*On the existence of capacitary strong type estimates in*, Ark. Mat.**14**(1976), 125-140. MR**0417774 (54:5822)****[2]**R. R. Coifman,*Distribution function inequalities for singular integrals*, Proc. Nat. Acad. Sci. U.S.A.**69**(1972), 2838-2839. MR**0303226 (46:2364)****[3]**B. Dahlberg,*Regularity properties of Riesz potentials*, Indiana Univ. Math. J.**28**(1979), 257-268. MR**523103 (80g:31004)****[4]**C. Fefferman,*Inequalities for strongly singular convolution operators*, Acta Math.**124**(1970), 9-36. MR**0257819 (41:2468)****[5]**K. Hansson,*Imbedding theorems of Sobolev type in potential theory*, Math. Scand.**45**(1979), 77-102. MR**567435 (81j:31007)****[6]**R. Kerman and E. Sawyer,*Weighted norm inequalities of trace-type for potential operators*, preprint.**[7]**V. G. Maz'ya,*On some integral inequalities for functions of several variables*, Problems in Math. Analysis, No. 3, Leningrad Univ. (Russian)**[8]**B. Muckenhoupt and R. L. Wheeden,*Weighted norm inequalities for fractional integrals*, Trans. Amer. Math. Soc.**192**(1974), 251-275. MR**0340523 (49:5275)****[9]**E. Sawyer,*Multipliers of Besov and power weighted**spaces*, Indiana Univ. Math. J. (to appear). MR**740955 (85f:42020)****[10]**E. M. Stein,*Singular integrals and differentiability properties of functions*, Princeton Univ. Press, Princeton, N.J., 1970. MR**0290095 (44:7280)**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
26A33,
26D10,
26D15,
42B25

Retrieve articles in all journals with MSC: 26A33, 26D10, 26D15, 42B25

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0719674-6

Article copyright:
© Copyright 1984
American Mathematical Society