{ "id": "1211.1084", "version": "v2", "published": "2012-11-06T00:49:09.000Z", "updated": "2012-11-09T03:18:50.000Z", "title": "Sharp spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates", "authors": [ "Peng Chen" ], "categories": [ "math.AP", "math.FA" ], "abstract": "We consider the abstract non-negative self-adjoint operator $L$ acting on $L^2(X)$ which satisfies Davies-Gaffney estimates and the corresponding Hardy spaces $H^p_L(X)$. We assume that doubling condition holds for the metric measure space $X$. We show that a sharp H\\\"ormander-type spectral multiplier theorem on $H^p_L(X)$ follows from restriction type estimates and the Davies-Gaffney estimates. We also describe the sharp result for the boundedness of Bochner-Riesz means on $H^p_L(X)$.", "revisions": [ { "version": "v2", "updated": "2012-11-09T03:18:50.000Z" } ], "analyses": { "keywords": [ "self-adjoint operators satisfying davies-gaffney estimates", "non-negative self-adjoint operators satisfying davies-gaffney", "sharp spectral multipliers", "hardy spaces" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2012arXiv1211.1084C" } } }