Abstract
Let L be a non-negative self-adjoint operator acting on L2(X) where X is a space of homogeneous type. Assume that L generates a holomorphic semigroup e-tL which satisfies generalized m-th order Gaussian estimates. In this article, we study singular and dyadically supported spectral multipliers for abstract self-adjoint operators. We show that in this setting sharp spectral multiplier results follow from Plancherel or Stein-Tomas type estimates. These results are applicable to spectral multipliers for a large class of operators including m-th order elliptic differential operators with constant coefficients, biharmonic operators with rough potentials and Laplace type operators acting on fractals.
Original language | English |
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Pages (from-to) | 368-409 |
Number of pages | 42 |
Journal | Journal of Functional Analysis |
Volume | 266 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2014 |