Projects per year
Abstract
We prove a quadratic sparse domination result for general nonintegral square functions S. That is, for p0 ∈ [1, 2) and q0 ∈ (2, ∞], we prove an estimate of the form
∫M(S f)2g dμ ≤ c ∑P∈S(−∫5P f p0 dμ)2/p0 (−∫5Pgq∗0 dμ)1/q∗0P,
where q∗ 0 is the Hölder conjugate of q0/2, M is the underlying doubling space and S is a
sparse collection of cubes on M. Our result will cover both square functions associated
with divergence form elliptic operators and those associated with the Laplace–Beltrami
operator. This sparse domination allows us to derive optimal norm estimates in the weighted space L p(w).
∫M(S f)2g dμ ≤ c ∑P∈S(−∫5P f p0 dμ)2/p0 (−∫5Pgq∗0 dμ)1/q∗0P,
where q∗ 0 is the Hölder conjugate of q0/2, M is the underlying doubling space and S is a
sparse collection of cubes on M. Our result will cover both square functions associated
with divergence form elliptic operators and those associated with the Laplace–Beltrami
operator. This sparse domination allows us to derive optimal norm estimates in the weighted space L p(w).
Original language  English 

Article number  20 
Number of pages  49 
Journal  Journal of Geometric Analysis 
DOIs  
Publication status  Published  14 Nov 2022 
Bibliographical note
Not yet published as of 14/11/2022.Keywords
 Elliptic operator
 Sparse bounds
 Sharp weighted estimates
 Square functions
Fingerprint
Dive into the research topics of 'Quadratic sparse domination and weighted estimates for nonintegral square functions'. Together they form a unique fingerprint.Projects
 1 Finished

Harmonic Analysis in rough environments
Engineering & Physical Science Research Council
1/03/17 → 30/04/20
Project: Research Councils