11 papers · 1 filter
Schatten classes and commutators in the two weight setting, II. Riesz transforms
Michael Lacey, Ji Li, Brett D. Wick +1
We characterize the Schatten class of the commutator of Riesz transforms in () in the two weight setting for , by introduc…
Quantitative Sobolev regularity of quasiregular maps
Francesco Di Plinio, A. Walton Green, Brett D. Wick
We quantify the Sobolev space norm of the Beltrami resolvent , where is the Beurling-Ahlfors transform, in terms of the corresponding Sobolev…
Schatten Class Estimates for Paraproducts in Multi-parameter setting and applications
Michael T. Lacey, Ji Li, Brett D. Wick
Let be a bounded parameter paraproduct with symbol . We demonstrate that this operator is in the Schatten class , , if the symbol is in the pa…
Weighted Estimates of Singular Integrals and Commutators in the Zygmund Dilation Setting
Xuan Thinh Duong, Ji Li, Yumeng Ou +2
The main purpose of this paper is to establish weighted estimates for singular integrals associated with Zygmund dilations via a discrete Littlewood--Paley theory, and then apply i…
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. Hytön…
Sparse domination results for compactness on weighted spaces
Cody B. Stockdale, Paco Villarroya, Brett D. Wick
By means of appropriate sparse bounds, we deduce compactness on weighted spaces, , for all Calderón-Zygmund operators having compact extensions on $L^2(\mathb…