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Proof of an extension of E. Sawyer’s conjecture about weighted mixed weak-type estimates
We show that if v ∈ A ∞ and u ∈ A 1 , then there is a constant c depending on the A 1 constant of u and the A ∞ constant of v such that T ( f v ) v L 1 , ∞ ( u v ) ≤ c ‖ f ‖ L 1 ( u v ) , where T can be the Hardy–Littlewood maximal function or any Calderón–Zygmund operator. This result was conjectur...
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| Published in: | Mathematische annalen 2019-06, Vol.374 (1-2), p.907-929 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | We show that if
v
∈
A
∞
and
u
∈
A
1
, then there is a constant
c
depending on the
A
1
constant of
u
and the
A
∞
constant of
v
such that
T
(
f
v
)
v
L
1
,
∞
(
u
v
)
≤
c
‖
f
‖
L
1
(
u
v
)
,
where
T
can be the Hardy–Littlewood maximal function or any Calderón–Zygmund operator. This result was conjectured in Cruz-Uribe et al. (Int Math Res Not 30:1849–1871,
2005
) and constitutes the most singular case of some extensions of several problems proposed by Sawyer and Muckenhoupt and Wheeden. We also improve and extends several quantitative estimates. |
|---|---|
| ISSN: | 0025-5831 1432-1807 |
| DOI: | 10.1007/s00208-018-1762-0 |