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Square function estimates on layer potentials for higher‐order elliptic equations

Square function estimates on layer potentials for higher‐order elliptic equations

Abstract In this paper we establish square‐function estimates on the double and single layer potentials for divergence form elliptic operators, of arbitrary even order 2 m , with variable t ‐independent coefficients in the upper half‐space. This generalizes known results for variable‐coefficient second‐order operators, and also for constant‐coefficient higher‐order operators.