Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896748 | Journal of Functional Analysis | 2018 | 21 Pages |
Abstract
In the context of local Tb theorems with Lp testing conditions we prove an enhanced Cotlar's inequality. This is related to the problem of removing the so called buffer assumption of Hytönen-Nazarov, which is the final barrier for the full solution of S. Hofmann's problem. We also investigate the problem of extending the Hytönen-Nazarov result to non-homogeneous measures. We work not just with the Lebesgue measure but with measures μ in Rd satisfying μ(B(x,r))â¤Crn, nâ(0,d]. The range of exponents in the Cotlar type inequality depend on n. Without assuming buffer we get the full range of exponents p,qâ(1,2] for measures with nâ¤1, and in general we get p,qâ[2âϵ(n),2], ϵ(n)>0. Consequences for (non-homogeneous) local Tb theorems are discussed.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Henri Martikainen, Mihalis Mourgoglou, Xavier Tolsa,