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math.CA2010
The Hilbert transform does not map L^1(Mw) to L^{1,\infty}(w)
Maria Carmen Reguera, Christoph Thiele
We prove that the analogue for the Hilbert transform of a classical weighted inequality by Fefferman and Stein for the Hardy Littlewood maximal operator does not hold. This is a se…
math.CA2010★ 1 cited
On Muckenhoupt-Wheeden Conjecture
Maria Carmen Reguera
Let M denote the dyadic Maximal Function. We show that there is a weight w, and Haar multiplier T for which the following weak-type inequality fails: $$ \sup_{t>0}t w\left\{x\in\ma…
math.CA2010★ 1 cited
Weak and Strong type Estimates for Calderón-Zygmund Operators
Tuomas P. Hytönen, Michael T. Lacey, Maria Carmen Reguera +3
For a Calderon-Zygmund operator T on d-dimensional space, that has a sufficiently smooth kernel, we prove that for any 1< p \le 2, and weight w in A_p, that the maximal truncations…