A Fractional Muckenhoupt–Wheeden Theorem and its Consequences
In the 1970s Muckenhoupt and Wheeden made several conjectures relating two weight norm inequalities for the Hardy-Littlewood maximal operator to such inequalities for singular integrals. Using techniques developed for the recent proof of the A 2 conjecture we prove a related pair of conjectures link...
Saved in:
Published in | Integral equations and operator theory Vol. 76; no. 3; pp. 421 - 446 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Basel
SP Birkhäuser Verlag Basel
01.07.2013
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | In the 1970s Muckenhoupt and Wheeden made several conjectures relating two weight norm inequalities for the Hardy-Littlewood maximal operator to such inequalities for singular integrals. Using techniques developed for the recent proof of the
A
2
conjecture we prove a related pair of conjectures linking the Riesz potential and the fractional maximal operator. As a consequence we are able to prove a number of sharp one and two weight norm inequalities for the Riesz potential. |
---|---|
ISSN: | 0378-620X 1420-8989 |
DOI: | 10.1007/s00020-013-2059-z |