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Square function and maximal function estimates for operators beyond divergence form equations

Andreas Rosén (Institutionen för matematiska vetenskaper)
Journal of Evolution Equations (1424-3199). Vol. 13 (2013), 3, p. 651-674.
[Artikel, refereegranskad vetenskaplig]

We prove square function estimates in L (2) for general operators of the form B (1) D (1) + D (2) B (2), where D (i) are partially elliptic constant coefficient homogeneous first-order self-adjoint differential operators with orthogonal ranges, and B (i) are bounded accretive multiplication operators, extending earlier estimates from the Kato square root problem to a wider class of operators. The main novelty is that B (1) and B (2) are not assumed to be related in any way. We show how these operators appear naturally from exterior differential systems with boundary data in L (2). We also prove non-tangential maximal function estimates, where our proof needs only off-diagonal decay of resolvents in L (2), unlike earlier proofs which relied on interpolation and L (p) estimates.

Nyckelord: DIRAC OPERATORS, ROOT PROBLEM, KATO



Denna post skapades 2013-09-13. Senast ändrad 2013-09-24.
CPL Pubid: 183313

 

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