76 citations · 360 across the 60 of their papers we have counts for
5 papers · 1 filter
The scalar theorem for pairs of doubling measures fails for Riesz transforms when p not 2
Michel Alexis, José Luis Luna-Garcia, Eric Sawyer +1
We show that for an individual Riesz transform in the setting of doubling measures, the scalar theorem fails when : for each , we…
The Hytönen-Vuorinen L^{p} conjecture for the Hilbert transform, with an extended energy side condition, when (4/3)<p<4 and the measures share no point masses
Eric T. Sawyer, Brett D. Wick
In the case (4/3)<p<4, and assuming a pair of locally finite positive Borel measures on the real line have no common point masses, we prove variants of two conjectures of T. Hytöne…
The Moser method and boundedness of solutions to infinitely degenerate elliptic equations
Lyudmila Korobenko, Cristian Rios, Eric Sawyer +1
We show that if is equipped with certain non-doubling metric and an Orlicz-Sobolev inequality holds for a special family of Young functions , then weak solution…
A reprise of the NTV conjecture for the Hilbert transform
Eric T. Sawyer
We give a slightly different proof of the NTV conjecture for the Hilbert transform that was proved by T. Hytönen, M. Lacey, E.T. Sawyer, C.-Y. Shen and I. Uriarte-Tuero, building o…
The T1 theorem for the Hilbert transform fails when p is not 2
Michel Alexis, Jose Luis Luna-Garcia, Eric T. Sawyer +1
Given p between 1 and infinity, but not 2, we show that the T1 theorem for the Hilbert transform fails for L^{p}, despite holding for p equal to 2