GENERALIZED LOCAL THEOREMS FOR SQUARE FUNCTIONS

Ana Grau de la Herrán, Steve Hofmann

Type: Article

Publication Date: 2016-07-25

Citations: 11

DOI: https://doi.org/10.1112/s0025579315000327

Abstract

A local theorem is an boundedness criterion by which the question of the global behavior of an operator is reduced to its local behavior, acting on a family of test functions indexed by the dyadic cubes. We present two versions of such results, in particular, treating square function operators whose kernels do not satisfy the standard Littlewood–Paley pointwise estimates. As an application of one version of the local theorem, we show how the solvability of the Kato problem (which was implicitly based on local theory) may be deduced from this general criterion.

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+	Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains	1984	Gregory C. Verchota
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