| Abstrakt: |
In this paper, we give a locally parabolic version of Tb theorem for a class of vector-valued operators with off-diagonal decay in L2 and certain quasi-orthogonality on a subspace of L2, in which the testing functions themselves are also vector-valued. As an application, we establish the boundedness of layer potentials related to parabolic operators in divergence form, defined in the upper half-space ℝ+n+2 ≔ {(x, t, λ) ∈ ℝn+1 × (0, ∞)}, with uniformly complex elliptic, L∞, t, λ-independent coefficients, and satisfying the De Giorgi/Nash estimates. [ABSTRACT FROM AUTHOR] |
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