A weighted weak-type bound for Haar multipliers
2018 ◽
Vol 148
(3)
◽
pp. 643-658
Keyword(s):
We study a weighted maximal weak-type inequality for Haar multipliers that can be regarded as a dual problem of Muckenhoupt and Wheeden. More precisely, if Tε is the Haar multiplier associated with the sequence ε with values in [−1, 1], and is the r-maximal operator, then for any weight w and any function f on [0, 1) we havefor some constant Cr depending only on r. We also show that the analogous result does not hold if we replace by the dyadic maximal operator Md. The proof rests on the Bellman function method; using this technique we establish related weighted Lp estimates for p close to 1, and then deduce the main result by extrapolation arguments.
Keyword(s):
2008 ◽
Vol 154
(2)
◽
pp. 161-180
◽
Keyword(s):
2009 ◽
Vol 125
(1-2)
◽
pp. 65-83
◽
2016 ◽
Vol 36
(2)
◽
pp. 359-370
◽
Keyword(s):
2021 ◽
Vol 58
(2)
◽
pp. 216-229
Keyword(s):
2013 ◽
Vol 61
(3)
◽
pp. 209-218