Weighted and Unweighted Solyanik Estimates for the Multilinear Strong Maximal Function
Let ω be a weight in A ∞ ∗ and let M n m ( f ) be the multilinear strong maximal function of f = f 1 , … , f m , where f 1 , … , f m are functions on R n . In this paper, we consider the asymptotic estimates for the distribution functions of M n m . We show that, for λ ∈ ( 0 , 1 ) , if λ → 1 - , the...
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| Veröffentlicht in: | Resultate der Mathematik 2021-03, Vol.76 (1), Article 6 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
ω
be a weight in
A
∞
∗
and let
M
n
m
(
f
)
be the multilinear strong maximal function of
f
=
f
1
,
…
,
f
m
, where
f
1
,
…
,
f
m
are functions on
R
n
. In this paper, we consider the asymptotic estimates for the distribution functions of
M
n
m
. We show that, for
λ
∈
(
0
,
1
)
, if
λ
→
1
-
, then the multilinear Tauberian constant
C
n
m
and the weighted Tauberian constant
C
n
,
ω
m
associated with
M
n
m
enjoy the properties that
C
n
m
(
λ
)
-
1
≃
m
1
-
λ
1
n
and
C
n
,
ω
m
(
λ
)
-
1
≲
m
(
1
-
λ
)
4
n
[
ω
]
A
∞
∗
-
1
. |
|---|---|
| ISSN: | 1422-6383 1420-9012 |
| DOI: | 10.1007/s00025-020-01317-x |