A sharp estimate on the norm of the martingale transform

By J. Wittwer. 2000

100 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5d726221a7bf1886c93a8e6055b0eeb7f395f69c

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In Applied Mathematics

Citations in the corpus

SHARP BOUNDS FOR GENERAL COMMUTATORS ON WEIGHTED LEBESGUE SPACES (2010, unknown): “The linear growth in L(2)(w) has been shown to hold for dyadic operators (martingale transform [34], dyadic square function [15], dyadic paraproduct [3]), or for operators that have lots of symmetries and can be written as averages of dyadic shift operators (such as the Hilbert transform [30], Riesz”
Linear bound for the dyadic paraproduct on weighted Lebesgue space L2(w) (2007, background): “It was also shown that the norm of the Martingale transform on the weighted space L2(w) depends linearly on the ‖w ‖A2 , see [Witt].”
Two Weight Inequalities for Discrete Positive Operators (2009, result): “And it has been subsequently used in the proofs of several results, such as [2, 14,15,24,25] among other papers.”
The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A p characteristic (2007, background): “For the next lemma we refer to [27]:”
Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular (2002, methodology): “Test functions are rather simple, so this program can be carried out. This has been done in [ 31 ].”
Sharp weighted estimates of the dyadic shifts and $A_2$ conjecture (2010, background): “Wittwer [43], who proved the A2 conjecture for the Haar mutipliers.”
Sharp weighted norm inequalities for Littlewood-Paley operators and singular integrals (2010, methodology): “[24] J. Wittwer, A sharp estimate on the norm of the martingale transform, Math.”
On $A_2$ conjecture and corona decomposition of weights (2010, methodology): “ost well used singular dyadic operator is called Martingale transform (see, e. g., [1], [2], [4]): for it, the sharp linear estimate in terms of A2 norm [w]A2 of the weight was obtained by Wittwer in [58]. The interesting feature of her proof was that she used as a template a two-weight Martingale t”
Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces (2005, background): “The connection is very well explained in the paper by Astala, Iwaniec and Saksman [AIS] who were interested in finding the minimal q W1 ,q loc still self-improve to belonging to”
Sharp A2 inequality for Haar shift operators (2009, background): “The operator T(σ·) is expanded in ‘Haar basis’, but as had been done prior papers, such as [7, 12, 16], the Haar bases are adapted to the two measures σ and μ.”
Sharp weighted estimates for classical operators (2010, background): “(w) ≤ Cpkαkℓ∞ [w] max(1, 1 p−1) Ap kfkLp(w). Furthermore, given a pair (u,v) that satisﬁes (1.2), then kTαfkLp(u) ≤ Ckαkℓ∞kfkLp(v). In the special case when αI = ±1, Theorem 1.7 was proved by Wittwer [56]. 10 DAVID CRUZ-URIBE, SFO, JOSE MAR´ ´IA MARTELL, AND CARLOS PEREZ´ Dyadic square functions. Le”