Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



The proof of the nonhomogeneous $ T1$ theorem via averaging of dyadic shifts

Author: A. Volberg
Original publication: Algebra i Analiz, tom 27 (2015), nomer 3.
Journal: St. Petersburg Math. J. 27 (2016), 399-413
MSC (2010): Primary 42B20
Published electronically: March 30, 2016
MathSciNet review: 3570958
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Once again, a proof of the nonhomogeneous $ T1$ theorem is given. This proof consists of three main parts: a construction of a random ``dyadic'' lattice as in two earlier papers by Nazarov, Treil, and Volberg, dated back to 2003 and 1997; an estimate for matrix coefficients of a Carderón-Zygmund operator with respect to random Haar basis if a smaller Haar support is good like in the paper of 1997 mentioned above; a clever averaging trick used by Hytönen, Peres, Treil, and Volberg in two papers of 2012 and 2014, which involves the averaging over dyadic lattices to decompose an operator into dyadic shifts eliminating the error term that was present in the random geometric construction employed in the papers of 2003 and 1997 mentioned above. Hence, a decomposition is established of nonhomogeneous Calderón-Zygmund operators into dyadic Haar shifts.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 42B20

Retrieve articles in all journals with MSC (2010): 42B20

Additional Information

A. Volberg
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan

Keywords: Operators, dyadic shift, $T1$ theorem, nondoubling measure
Received by editor(s): November 20, 2014
Published electronically: March 30, 2016
Dedicated: To Nina Ural’tseva who taught me Mathematical Physics and how to zoom in on its beauty
Article copyright: © Copyright 2016 American Mathematical Society